The Central Limit Theorem is a statistical concept that describes the behavior of sample means when samples are taken from a population with any distribution. It states that as the sample size increases, the distribution of sample means will approach a normal distribution regardless of the shape of the original population distribution.
In other words, the sampling distribution of the sample mean will become approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
This theorem is important in statistics because it allows us to use the properties of the normal distribution to make inferences about the population mean, even if we do not know the population distribution. It also provides a basis for hypothesis testing and confidence interval estimation.
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how much did the naming rights for the 122 teams in the four major us professional sports leagues earn for those franchises in 2009
In 2009, the naming rights for the 122 teams in the four major US professional sports leagues (NFL, NBA, MLB, and NHL) earned those franchises approximately $3.6 billion.
In 2009, the naming rights deals for the 122 teams across the NFL, NBA, MLB, and NHL generated approximately $3.6 billion for those franchises. These deals allow companies to attach their name to a stadium or arena, which can provide valuable exposure and brand recognition.
The amount earned from these deals can vary widely based on factors such as the popularity of the team and the location of the stadium or arena. Despite fluctuations in the economy and the sports industry, naming rights deals have remained a significant source of revenue for professional sports franchises.
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1. [16 marks You are a member of a team of quality assurance specialists. Your team's immediate objective is to determine whether a product meets engineering design specifications provided by the product design team. Your team gathers a sample of 49 units of product, and you measure the height of each unit, in millimetres. + a) [1 mark] Find the sample mean of these 49 units. 2.1 3. Do not round your answer. Enter your command and your final answer in the space below. For example, if you were instead calculating the sample standard deviation, and the data were in cells A1:A49, your command and your final answer would be ustdev.s(A1:A49)= number. I b) [4 marks] Suppose the population standard deviation is 5 millimetres, and the engineering design specifications state that the population mean height must be at least 90 mm. What is the probability of obtaining a sample mean height of at least 2 (calculated from part a) of this question), if the population mean height is at least 90 mm? Declare the random variable of interest, show the probability you are asked to calculate and any tricks you might choose to use), how you standardize, your Z-score, and your final answer rounded to 4 decimal places. Hint: use u = 90 in your calculation. + c) [6 marks] Calculate 68%, 95%, and 99.7% tolerance intervals for the sample mean height, and interpret each of your intervals. Since you know its value, use the population standard deviation () instead of the sample standard deviation (S). Do not round your answers. Show your work. 1 d) [2 marks] Suppose the product design team changes their design specification: now, they say that at least 95% of all units of product must have a height of at least 95mm. Based on your tolerance intervals from part c), do you believe that the new design specification is being met? Why or why not? Please answer in at most 3 sentences. e) [3 marks] Suppose your team collects a new sample with 150 units. Notice the population standard deviation does not change, so your tolerance intervals from part c) still apply. How many units from your new sample of 150 do you expect to lie in your 68% tolerance interval? Your 95% tolerance interval? Your 99.7% tolerance interval? Do not round any of your answers. Show your work: show cach distribution you use, how you calculate your answers, and your final answers.
the product of 3/4 and c
Answer:
3/4c
Step-by-step explanation:
"The product of 3/4 and c" is represented by the phrase 3/4c.
Mathematical expressions are sentences that have a minimum of two numbers or variables, at least one arithmetic operation, and the term.
The phrase "the product of 3/4 and c" is presented here.
We now need to come up with a good expression for this.
The following are offered as a result of our analysis of the provided statement.
3/4 is a reference to a number, or a constant.
C stands for the variable.
The mathematical procedure between a number and a variable is referred to as the product.
Hence, it can be written as per the accepted manner of expression.
=> 3/4 x c
=> 3/4 c
ACT scores. The scores of students on the ACT college entrance examination in a recent year had a Normal distribution. with mean µ = 18.6 and a standard deviation of σ = 5.9.What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?Now take a simple random sample of 50 students who took the test. What are the mean and standard deviation of the sample mean score ¯x of these 50 students?What is the probability that the mean score of these students is 21 or higher?
the probability corresponding to this z-score in a standard normal distribution table, we find that the probability of the mean score of these 50 students being 21 or higher is 0.0319 or about 3.2%.
The first part of the question asks for the probability that a single student is randomly chosen from all those taking the test scores 21 or higher. To solve this, we need to find the z-score corresponding to a score of 21 or higher, using the formula:
z = (x - µ) / σ
where x is the score, µ is the mean, and σ is the standard deviation. Substituting the given values, we get:
z = (21 - 18.6) / 5.9 = 0.41
Looking up the probability corresponding to this z-score in a standard normal distribution table, we find that the probability of a student scoring 21 or higher is 0.3393 or about 34%.
Next, we are asked to find the mean and standard deviation of the sample mean score of 50 students. Since the sample size is sufficiently large (n ≥ 30), we can use the Central Limit Theorem to approximate the sample mean as normally distributed, with mean equal to the population mean (µ = 18.6) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ / √n = 5.9 / √50 = 0.835). Therefore, the mean of the sample mean score ¯x is also 18.6, and the standard deviation is 0.835.
Finally, we need to find the probability that the mean score of these 50 students is 21 or higher. We can again use the formula for the z-score:
z = (x - µ) / (σ / √n)
Substituting the given values, we get:
z = (21 - 18.6) / (5.9 / √50) = 1.86
Looking up the probability corresponding to this z-score in a standard normal distribution table, we find that the probability of the mean score of these 50 students being 21 or higher is 0.0319 or about 3.2%.
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Someone please help me out
Answer:
1/36
Step-by-step explanation:
There are a total of 36 possible combinations. Of those 36 combinations, only 1 would result in rolling two 2's.
Therefore, the probability would be 1 [outcome]/36 [total outcomes], which cannot be simplified any further.
The probability that an individual is left-handed is 0.15. In a class of 30 students, what is the probability of finding five left-handers?
From the binomial probability distribution the probability of finding five left-handers in a class of 30 students is equals to the 0.1861.
We have a class of total 30 students. Let's consider an event be X : students who are left-handed in class.
Total possible outcomes or results, n = 30
The probability that an individual is left-handed students, P(X) = 0.15 that is probability of success, p = 0.15
Probability of failure, q = 1 - p = 1 - 0.15
= 0.85
We have to determine probability of finding five left-handers, P( X = 5). Using the binomial Probability distribution formula is written as
P( X = x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾
where, x --> observed value
n --> number of trials
p --> probability of success
Now, plug all known values in above formula, P( X = 5) = ³⁰C₅ p⁵ (1-p)³⁰⁻⁵
= ³⁰C₅ (0.15)⁵ (0.85)²⁵
= 142,506 × 0.0000013059
= 0.1861
Hence, required value is 0.1861.
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1. Ben wrote a report on trains.
Author's Reason:
Explain:
Answer:
Step-by-step explanation:
the answer is 2 because if you subtract and add you will get your and and good luck on the state test 5th 6th and 7th and younger kids.
What is the value of x?
(8x + 6)
102°
▸
The value of x in the equation is 9
How to determine the valueFrom the information given, we have that the angles are supplementary.
Then, it is important that we note the definition of supplementary angles.
Supplementary angles are simply defined as pair of angles that sum to 180 degrees. They must be two angles.
Also, angles on a straight line is equal to 180 degrees.
From the information given, we have that;
8x + 6 and 102 degrees are supplementary.
Then,
8x + 6 + 102 = 180
collect the like terms, we get;
8x = 180 - 108
subtract the values
8x = 72
x = 9
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Question
If the angles are supplementary, What is the value of x?
(8x + 6)
102°
▸
If the numbers belong to a population, in symbols a deviation is x - μ. For sample data, in symbols a deviation is x - x¯.
If the numbers belong to a population, in symbols a deviation is x - μ. For sample data, in symbols, a deviation is x - x¯. True
The standard deviation is a gauge of how evenly distributed a set of numbers is. Since total variance is general average of squared deviations from the mean, it is the square root of the variance. Further, The deviation is a statistic that expresses how distant a single data point is from a mean, such as the population mean (denoted by u ) or sample mean (denoted by x ).
For a population, x - represents the difference between a data point's departure from the population mean. When using sample data, the difference between a data point (x) and the sample mean (x) is calculated as follows: x - x, where x is the average of the sample data.
Complete Question:
If the numbers belong to a population, in symbols a deviation is x - μ. For sample data, in symbols, a deviation is x - x¯. True/False
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Larry started the following number pattern: 900, 888, 876, 864, ...Which number could not be a part of Larry's pattern? A. 756 B. 816 C. 736 D. 624
816 cannot be part of Larry's pattern, since it is not obtained by subtracting 12 from the previous term. Therefore, the answer is B.
In Larry's number pattern, each term is obtained by subtracting 12 from the previous term. We can check whether each of the given answer choices can be part of Larry's pattern by performing this subtraction:
900 - 12 = 888
888 - 12 = 876
876 - 12 = 864
756 - 12 = 744
816 - 12 = 804
736 - 12 = 724
624 - 12 = 612
Therefore, 816 could not be a part of Larry's pattern
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Cory mowed lawns for $35 per lawn. Which representation shows the amount of money Cory earned at this rate?
The representation shows the amount of money Cory earned at this rate is f(x) = $35x
The representation that shows the amount of money Cory earned at this rateOne possible representation to show the amount of money Cory earned at the rate of $35 per lawn is:
Let "n" be the number of lawns mowed by Cory.
The amount of money he earned would then be:
$35n
Another possible representation is using a function:
Let "f(x)" be the amount of money Cory earned after mowing "x" lawns.
Then: f(x) = $35x
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Suppose the cumulative distribution function of the random variable X is Find the value of P(X>5).
For a cumulative distribution function of the random variable X defined as
[tex]F(x) = \left\{ \begin{array}{ll} 0 & \quad x < 0 \\0.2 x & \quad0 \leqslant x < 5 \\ 1 & \quad5 \leqslant x \end{array} \right.[/tex] the probability value of P(X>5) is equals to the 0.
The cumulative distribution function (CDF) is used to the probabilities of a random variable with values less than or equal to x. It describe the probability for a discrete, continuous or mixed random variable. The cumulative distribution function (CDF) of random variable X is written as F(x) = P(X≤x), for all x∈R.
We have a random variable X, the cumulative distribution function of the variable X is written as [tex]F(x) = \left\{ \begin{array}{ll} 0 & \quad x < 0 \\0.2 x & \quad0 \leqslant x < 5 \\ 1 & \quad5 \leqslant x \end{array} \right.[/tex]
We have to determine value of probability P( X> 5) . As we know, P( X > 5) = 1 - P( X ≤ 5)
= 1 - F( 5)
= 1 - 1
= 0
Hence, required value is equals to the 0.
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Complete question :
The above figure complete the question
Suppose the cumulative distribution function of the random variable X is present in above figure. Find the value of P(X>5).
The functions f(x) and g(x) are represented by the following table and graph. Compare the functions, and then answer the question.
(graph and table and options are attached below)
Which statements about the functions are true?
There is more than one correct answer. Select all correct answers
Responses
1. g(x)
goes to positive infinity as x
approaches negative infinity, so there is no maximum value.
g of x goes to positive infinity as x approaches negative infinity, so there is no maximum value.
2. f(x)
is a line that approaches positive infinity as x
approaches positive infinity, so there is no maximum value.
f of x is a line that approaches positive infinity as x approaches positive infinity, so there is no maximum value.
3. g(x)
goes to negative infinity as x
approaches negative infinity, so there is no minimum value.
g of x goes to negative infinity as x approaches negative infinity, so there is no minimum value.
4. f(x)
is a line that approaches positive infinity as x
approaches negative infinity, so there is no maximum value.
f of x is a line that approaches positive infinity as x approaches negative infinity, so there is no maximum value.
5. f(x)
is a line that approaches negative infinity as x
approaches negative infinity, so there is no minimum value.
f of x is a line that approaches negative infinity as x approaches negative infinity, so there is no minimum value.
6. g(x)
has a horizontal asymptote at y=0,
so the minimum is almost at 0
for any interval that includes x
values greater than zero but doesn't go to positive infinity.
g of x has a horizontal asymptote at y is equal to 0 textsf comma so the minimum is almost at 0 for any interval that includes x values greater than zero but doesn't go to positive infinity.
7. f(x)
is a line that approaches negative infinity as x
approaches positive infinity, so there is no minimum value.
f of x is a line that approaches negative infinity as x approaches positive infinity, so there is no minimum value.
8. g(x)
has a horizontal asymptote at y=1,
so the minimum is almost at 1
for any interval that includes x
values greater than zero but doesn't go to positive infinity.
The graph of the functions f(x) and g(x) shows that f(x) is a straight line that increases as x increases, while g(x) is a parabola that increases as x increases. Therefore, all of the statements given are true.
What is asymptote?An asymptote is a straight line or curve that approaches a given curve arbitrarily closely but never meets or crosses it.
The correct answers are 1, 2, 3, 4, 5, 6, 7 and 8.
The graph of the functions f(x) and g(x) shows that f(x) is a straight line that increases as x increases, while g(x) is a parabola that increases as x increases.
From the table and graph, it is clear that both functions go to positive and negative infinity as x approaches positive and negative infinity, respectively, so there is no maximum or minimum value for either function.
Additionally, both functions have a horizontal asymptote at y=0 and y=1 for x values greater than zero but not going to positive infinity.
This means that the minimum for g(x) is almost at 0 and the minimum for f(x) is almost at 1. Therefore, all of the statements given are true.
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-2(-6x + 3y - 1)
Use the distributive property to write an expression.
Answer:
12x-6y+2
Step-by-step explanation:
-2 (-6x) -2 (3y) -2 x -1
12x - 6y - 2 x -1
12x-6y+2
What are the possible results that you could have with a Pearson's product-moment correlation?
A Pearson's product-moment correlation can result in a coefficient ranging from -1 to 1, with 0 indicating no correlation and positive or negative values indicating the direction and strength of the correlation.
A coefficient close to 1 or -1 indicates a strong correlation, while a coefficient close to 0 indicates a weak correlation. It is important to note that correlation does not imply causation and that the results should be interpreted with caution. Additionally, the validity of the results depends on the quality of the data and the content loaded into the analysis.
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Question 1(Multiple Choice Worth 5 points) (Appropriate Measures MC) The table shows the number of runs earned by two baseball players. Player A Player B 2, 1, 3, 8, 2, 3, 4, 3, 2 2, 3, 1, 4, 2, 2, 1, 4, 6 Find the best measure of variability for the data and determine which player was more consistent. I need this ASAP
The best measure of variability for the data is the standard deviation the player that more consistent is Option B: Player B.
What is standard deviation?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
The best measure of variability for this data would be the standard deviation.
To determine which player was more consistent, we need to calculate the standard deviation for each player's data set.
For Player A, the mean is 3 and the standard deviation is 2.
For Player B, the mean is 2.44 and the standard deviation is 1.41.
Since Player B has a lower standard deviation, they are more consistent than Player A.
Therefore, the correct answer is -
Option B: Standard deviation; Player B was more consistent.
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A circle graph has four sections. One section makes up 45% of this circle graph. Determine the central angle measurement. Question 2 options: 162° 16,200° 8° 360°
The central angle measurement of the section that makes up 45% of the circle graph is 162 degrees. Answer: 162°
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
According to the given information:If one section makes up 45% of the circle graph, then the other three sections combined make up the remaining 55% of the graph. Since the circle graph represents a full circle, which has a total central angle measurement of 360 degrees, we can set up the following proportion:
45/100 = x/360
where x is the central angle measurement of the section that makes up 45% of the graph. To solve for x, we can cross-multiply and simplify:
45 * 360 = 100 * x
x = 16,200/100
x = 162
Therefore, the central angle measurement of the section that makes up 45% of the circle graph is 162 degrees. Answer: 162°
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A mouse pushes a block of cheese across the floor with 4 N of force. How many meters did the mouse travel if she did 16 J of work?
The mouse traveled 4 meters while pushing the block of cheese with 4 N of force if she did 16 J of work.
What is equations?An equation is a mathematical statement that shows that two expressions are equal. Equations typically consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
According to the given information:We know that work (W) is equal to force (F) times distance (d) in the direction of the force, so we can use the formula:
W = F x d
To find the distance traveled (d), we need to rearrange the formula:
d = W / F
Plugging in the values we have:
d = 16 J / 4 N
d = 4 meters
Therefore, the mouse traveled 4 meters while pushing the block of cheese with 4 N of force, if she did 16 J of work.
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(18 points) Determine the order of the following PDEs, and state whether they are linear and homogeneous (a). yềuxx + xuyy = 0 (b). (x + y) +e^x+xyday = 0 (c). Uyu: + ux = Uxyz + xyz
The order of the PDEs, their linearity, and homogeneity are:
(a) Order: 2, Linear, Homogeneous
(b) Order: 1, Non-linear, Inhomogeneous
(c) Order: 3, Linear, Homogeneous
(a) yuxx + xuyy = 0
This PDE has second-order partial derivatives (uxx and uyy). It is linear because the highest power of u or its derivatives is 1. It is homogeneous because there are no terms without u or its derivatives.
(b) (x + y)u + eˣ + xyday = 0
This PDE has a first-order partial derivative (day). It is non-linear because the term xyday contains a product of u and a dependent variable (y). It is inhomogeneous because of the eˣ term, which does not contain u or its derivatives.
(c) Uyu + ux = Uxyz + xyz
This PDE has third-order partial derivatives (Uxyz). It is linear because the highest power of u or its derivatives is 1. It is homogeneous because there are no terms without u or its derivatives.
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Determine whether the statement is true or false.If f '(x) > 0 for 3 < x < 5, then f is increasing on (3, 5)
The statement that "If function f '(x) > 0 for 3 < x < 5, then f is increasing on (3, 5)" is determined to be True.
If the derivative of a function f is positive on an interval, it means that the slope of the function is positive on that interval. This, in turn, means that the function is increasing on that interval. Therefore, if f '(x) > 0 for 3 < x < 5, then f is increasing on (3, 5).
The statement is based on the fact that the derivative of a function represents its instantaneous rate of change or slope. When the derivative is positive, the function is increasing, meaning that its output values are getting larger as its input values increase.
Thus, if f '(x) > 0 for 3 < x < 5, it implies that the slope of f is positive on the interval (3, 5), and therefore, f is increasing on that interval.
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Suppose you want to test the claim that μ ≠3.5. Given a sample size of n = 51 and a level of significance of. When should you reject H0 ?
The calculated t-value is between -2.009 and 2.009, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that μ ≠3.5.
To test the claim that μ ≠3.5, we need to perform a hypothesis test.
The null hypothesis (H0) is that μ = 3.5, and the alternative hypothesis (Ha) is that μ ≠3.5.
We have a sample size of n = 51, and a level of significance of α = 0.05.
We can use a t-test for the mean with unknown population standard deviation since we do not know the population standard deviation.
The test statistic is calculated as:
t = (x - μ) / (s / √(n))
Where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
If the calculated t-value is greater than the critical t-value for a two-tailed test with α = 0.05 and degrees of freedom = n - 1, we reject the null hypothesis.
The critical t-value for a two-tailed test with α = 0.05 and degrees of freedom = 50 (n - 1) is ± 2.009.
Therefore, if the calculated t-value is less than -2.009 or greater than 2.009, we reject the null hypothesis and conclude that there is evidence to support the claim that μ ≠3.5.
If the calculated t-value is between -2.009 and 2.009, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that μ ≠3.5.
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A random sample of 150 students has a grade point average with a mean of 2.86 and with a population standard deviation of 0.78. Construct the confidence interval for the population mean, μ. Use a 98% confidence level.
The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).
In order to construct a 98% confidence interval, follow these steps:1: Identify the given data
Sample size (n) = 150 students
Sample mean (x) = 2.86
Population standard deviation (σ) = 0.78
Confidence level = 98%
2: Find the critical z-value (z*) for a 98% confidence level
Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).
3: Calculate the standard error (SE)
SE = σ / √n
SE = 0.78 / √150 ≈ 0.064
4: Calculate the margin of error (ME)
ME = z* × SE
ME = 2.33 × 0.064 ≈ 0.149
5: Construct the confidence interval
Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711
Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009
The 98% confidence interval is approximately (2.711, 3.009).
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What is the slope of the line tangent to the curve 3y²-2x²=6-2xy at ( 3 , 2 )
The slope of the tangent line to the curve at the point (3, 2) is 7/6.
To find the slope of the tangent line to the curve at a point, we need to take the derivative of the curve with respect to x and evaluate it at that point.
We can start by rearranging the equation of the curve to get it in terms of y:
3y² = 2x² + 2xy - 6
Next, we can take the derivative of both sides with respect to x:
6y * dy/dx = 4x + 2y * dx/dx
Simplifying:
dy/dx = (4x + 2y) / (6y)
Now we can evaluate this expression at the point (3, 2):
dy/dx = (4(3) + 2(2)) / (6(2)) = 14/12 = 7/6
Therefore, the slope of the tangent line to the curve at the point (3, 2) is 7/6.
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Danielle surveyed her classmates about the number of movies they saw over summer break. Here are the results
0,0,1,1,2,2,4,5,6,6,8,10,12,12,14
The results of a poll Danielle conducted among her classmates regarding the amount of movies they saw during the summer are listed below in Numerical order: 0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 8, 10, 12, 12, 14.
What is ascending numerical order?
Numbers are organized from smallest to largest when they are placed in ascending order. Before we can put the numbers in any order, we must first compare the numbers.
Compare before ordering. In descending sequence, the following numbers: Count the number of digits in each number.
Numerical order: 0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 8, 10, 12, 12, 14.
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the fair isaac corporation credit score is used by banks and other lenders to determine whether someone is a good credit risk. scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. an economist wants to determine whether the mean fico score is lower than the cutoff of 720. she finds that a random sample of 60 people had a mean fico score of 695 with a standard deviation of 65. can the economist conclude that the mean fico score is less than 720? use the a
The economist can conclude that the mean FICO score is less than 720 with a 95% confidence level.
To answer this question, we can use a one-sample t-test with a significance level of α=0.05.
First, we need to calculate the t-statistic:
t = (sample mean - hypothesized mean) / (standard deviation / √(sample size))
t = (695 - 720) / (65 / sqrt(60))
t = -2.81
Next, we need to find the critical t-value using a t-distribution table with 59 degrees of freedom (sample size - 1) and a significance level of α=0.05.
The critical t-value is -1.67 (one-tailed test).
Since the calculated t-statistic (-2.81) is less than the critical t-value (-1.67), we can reject the null hypothesis and conclude that the mean FICO score is significantly lower than 720. In other words, based on the sample data, the economist can conclude that the mean FICO score is less than 720 with a 95% confidence level.
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An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 5 dollars per square foot and the cost to construct the four sides is 3 dollars per square foot, determine the dimensions for a box to have volume = 25 cubic feet which would minimize the cost of construction.
height =
dimensions of the base =
The dimensions of the base are [tex]25 \sqrt{2} by 100/ \sqrt{2}[/tex], and the height of the box is [tex]5 \sqrt{2}[/tex]
Let's start by defining the variables we need:
L: length of the base
W: width of the base
H: height of the box
From the problem statement, we know that:
L = 4W (the length of the base is 4 times larger than the width)
V = LWH = 25 (the volume of the box is 25 cubic feet)
We want to minimize the cost of construction, which is composed of two
parts: the cost of the base and the cost of the four sides.
Let's write expressions for these costs:
Cost of the base: 5LW
Cost of the four sides: 4WH + 2LH
The total cost is then:
C = 5LW + 3(4WH + 2LH)
Substituting L = 4W and V = LWH = 25, we get:
C = 5(4W)W + 3(4W)(25/4W) + 3(2H)(25/W)
Simplifying and factoring out 25, we get:
C = 75 + 30W + 150/H
To minimize C, we need to find the values of W and H that minimize this expression. We can use calculus for that:
[tex]dC/dW = 30 - 150/H^2 = 0[/tex]
[tex]dC/dH = -150W/H^2 = 0[/tex]
From the second equation, we can see that either W = 0 or H = 0, which is not physically meaningful. So we must have:
W = 5H
Substituting this into the first equation, we get:
[tex]30 - 150/H^2 = 0[/tex]
Solving for H, we get:
[tex]H = \sqrt{ (150/3)} = 5 \sqrt{2}[/tex]
Substituting this into W = 5H, we get:
[tex]W = 25 \sqrt{2}[/tex]
Finally, we can use L = 4W and V = LWH = 25 to find:
[tex]L = 100/ \sqrt{2} \\H = 5 \sqrt{2} \\W = 25 \sqrt{2}[/tex]
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Mr. Habib bought 8 gifts. If he spent between $2 and $5 on each gift, which is a reasonable total amount that Mr. Habib spent on all of the gifts? A. Under $10 B. $45 C. $32 D. More than $50
The reasonable total amount spend by Mr. Habib is $32 under the condition that the total number of gifts was 8 which ranged from $2 and $5 on each gift. Then the required correct option is Option C.
To evaluate the following question we have to implement basic multiplication of numbers
In case of spending $2 for each gift
Amount Spend = 2× 8 = $16
In case of spending $5 for each gift
Amount Spend = 5×8 = $40
So when we compare the amounts generated after choosing any one of the given cases, the in between option that is suitable and meets the criteria is $32.
The reasonable total amount spend by Mr. Habib is $32 under the condition that the total number of gifts was 8 which ranged from $2 and $5 on each gift. Then the correct option is Option C.
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Assuming that the homoskedastic normal regression assumption hold, find the critical value for the following situations: (a) n=28, 5% significance level, one-sided test. (b) n=40, 1% significance level, two-sided test. (c) n=10, 10% significance level, one-sided test. (d) n= 0,5% significance level, two-sided test.
Assuming the homoskedastic normal regression assumption holds, the critical value can be calculated using the t-distribution.
(a) n=28, 5% significance level, one-sided test
1. Determine the degrees of freedom: df = n-2 = 28-2 = 26
2. Look up the critical value in a t-distribution table for a 5% significance level and 26 degrees of freedom (one-sided): t-critical = 1.706
(b) n=40, 1% significance level, two-sided test
1. Determine the degrees of freedom: df = n-2 = 40-2 = 38
2. Look up the critical value in a t-distribution table for a 1% significance level and 38 degrees of freedom (two-sided): t-critical = 2.712
(c) n=10, 10% significance level, one-sided test
1. Determine the degrees of freedom: df = n-2 = 10-2 = 8
2. Look up the critical value in a t-distribution table for a 10% significance level and 8 degrees of freedom (one-sided): t-critical = 1.397
(d) Since n=0 in this situation, it is impossible to calculate a critical value. The sample size should be greater than 0 for a meaningful test.
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One of the ways in which doctors try to determine how long a single dose of pain reliever will provide relief is to measure the drug’s half-life, which is the length of time it takes for one-half of the dose to be eliminated from the body. A report of the National Institutes of Health states that the standard deviation of the half-life of the pain reliever oxycodone is σ =1.43 hours. Assume that a sample of 25 patients is given the drug, and the sample standard deviation of the half-lives was s =1.5 hours. Assume the population is normally distributed. Can you conclude that the true standard deviation is greater than the value reported by the National Institutes of Health?
We cannot conclude that the true standard deviation is greater than the value reported by the National Institutes of Health.
To answer this question, we need to conduct a hypothesis test. The null hypothesis is that the true standard deviation of the half-life of oxycodone is equal to 1.43 hours (σ = 1.43). The alternative hypothesis is that the true standard deviation is greater than 1.43 hours (σ > 1.43). We will use a one-tailed test with a significance level of 0.05.
To perform the test, we need to calculate the test statistic, which is given by:
t = (s / sqrt(n-1)) / (σ0 / sqrt(n))
where s is the sample standard deviation (1.5 hours), n is the sample size (25), and σ0 is the hypothesized value of the standard deviation (1.43 hours).
Plugging in the values, we get:
t = (1.5 / sqrt(24)) / (1.43 / sqrt(25)) = 1.49
Using a t-distribution table with 24 degrees of freedom and a significance level of 0.05, we find the critical value to be 1.711. Since our calculated t-value (1.49) is less than the critical value (1.711), we fail to reject the null hypothesis.
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A dorm at a college houses 1900 students. One day, 20 of the students become ill with the flu, which spreads quickly. Assume that the total number of students who have been infected 1900 after t days is given by N(t) = 1 + 12 e - 0.95 a) After how many days is the flu spreading the fastest? b) Approximately how many students per day are catching the flu on the day found in part (a)? c) How many students have been infected on the day found in part (a)? ..... a) The flu is spreading the fastest after days. (Do not round until the final answer. Then round to two decimal places as needed.)
Once more, since there is no solution to this equation, N(t) lacks an inflection point. As a result, the flu is spreading continuously; there is no particular day when it is spreading the quickest.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
We must locate the largest value of the function N(t) with respect to t in order to determine the day on which the illness is spreading the quickest.
[tex]N(t) = 1 + 12e^(-0.95t)\\N'(t) = -11.4e^(-0.95t)\\-11.4e^{(-0.95t)} = 0\\e^{(-0.95t)} = 0\\[/tex]
Since there is no answer to this equation, there is no maximum or lowest value for N(t). However, by calculating the second derivative of N(t) with respect to t, we can determine the inflection point of N(t):
[tex]N''(t) = 10.83e^(-0.95t)\\10.83e^(-0.95t) = 0\\e^(-0.95t) = 0\\[/tex]
Once more, since there is no solution to this equation, N(t) lacks an inflection point. As a result, the flu is spreading continuously; there is no particular day when it is spreading the quickest.
No one day sees a greater spread of the flu.
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