Answer: 360 cubic centimeters.
Step-by-step explanation:
Since it has a base shaped like a square and we know that it has a side length of 6 cm then we could square it an multiply it by the height.
6^2 = 36
36 * 10 = 360
The U.S. Department of Housing and Urban Development publishes data on the fair market monthly rent for existing one-bedroom housing by metropolitan area (The Federal Register, April 30 1997). The standard deviation for the monthly rent is about $80. Assume that a sample of metropolitan areas will be selected in order to estimate the population mean of the monthly rent for existing one-bedroom housing. Use 95% confidence. a. How large should the sample be if the desired margin of error is $25?
Answer:
[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]
So the answer for this case would be n=247 rounded up to the nearest integer
Step-by-step explanation:
We know that the standard deviation is :
[tex]\sigma = 80[/tex] represent the deviation
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution and the critical value would be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]
So the answer for this case would be n=247 rounded up to the nearest integer
An intravenous fluid is infused at the rate shown in the table. What is the missing value?
Minutes
Milliliters
3
ܢܚܪ
2.
?
3
9
4
12
3
6
9
24
Answer:
the answer is 6!!!!!!
Step-by-step explanation:
The missing value in the table is 5
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
An intravenous fluid is infused at the rate shown in the table
Minutes Milliliters
3 4
? 12
2. 3
? 6
3 9
9 24
Slope=24-9/9-3
=15/3
=5
Now 5=12-4/x-3
5=8/x-3
5x-15=8
5x=23
x=23/5
x=4.6
x=5
The missing number is 5.
Hence, the missing value in the table is 5
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Isaac is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is
x
= 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Isaac runs.
(a) 15.01 to 19.99 miles (b) 15.07 to 19.93 miles
(c) 15.34 to 19.66 miles (d) 15.31 to 19.69 miles
(e) 15.08 to 19.92 miles
Answer: (b) 15.07 to 19.93 miles
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 3.8
n = number of samples = 20
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 20 - 1 = 19
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.02/2 = 0.005
the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.861
Margin of error = 2.861 × 3.8/√20
= 2.43
the lower limit of this confidence interval is
17.5 - 2.43 = 15.07 miles
the upper limit of this confidence interval is
17.5 + 2.43 = 19.93 miles
3. Match each staternent with an expression that could be used to find the price
p+ 0.3p
0.7p
e. 85% more than the original time
f 15% less time than the original
g. 85% time decrease
h, 15% time increase
17p
p-07p
I
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expres
find the amount of money in his bank? Let "m" represent the original
Answer:
3a) 30% more than original price
b) 70% of the original price
c) 17times the original price
d) 70% less than original price
e) t + 0.85t
f) t - 0.15t
g) t - 0.85t
h) t + 0.15t
4. The expression that can be used to find the amount of money in his bank = m + 0.25m
Question:
3. Match each statement with an expression that could be used to find the price.
'The expressions for a to d were not stated in the question'.
a) p+ 0.3p
b) 0.7p
c) 17p
d) p-07p
'From e to h, we were not told what to determine'.
Write the expression in terms of time
e. 85% more than the original time
f. 15% less time than the original
g. 85% time decrease
h. 15% time increase
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original.
Step-by-step explanation:
let original price = p
a) p+ 0.3p = p + 30% of p
30% more than original price
b) 0.7p = 70% of p
= 70% of the original price
c) 17p = 17 × p
= 17times of the original price
d) p-0.7p = p - 70% of p
= 70% less than original price
Let original time = t
e) 85% more than the original time = t + 85%of t
= t + 0.85t
f) 15% less time than the original time = t - 15% of t
= t - 0.15t
g) 85% time decrease = t - 85% of t
= t - 0.85t
h) 15% time increase = t + 15% of t
= t + 0.15t
4. Since "m" represent the original amount in Hus piggy bank
An increase of 25% = original amount + 25% of original amount
= m + 25% of m
'Of' means multiplication
= m + 0.25 ×m
= m + 0.25m
= 1.25m
The expression that can be used to find the amount of money in his bank = m + 0.25m
A car dealership decreased the price of a certain car by 4% . The original price was $43,600 . write the new price in terms of the original price.
Answer: The new price of the car is $41856
Step-by-step explanation:
So we know the the original price as 43,600 which is 100% and is being dropped by 4% so you would have to subtract 4% from a 100% and multiply it by the original price.
100% - 4% = 96%
Now 96% of the original price is the new price.
96% * 43,600= ?
0.96 * 43,600 = 41856
luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how
Answer:
The speed of the river is 2mph.
Step-by-step explanation:
I guess that we want to find the speed of the river.
First, remember the relation: speed*time = distance
If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:
Sd = 4mph + Sr
and at this speed, in a time T, she can move 21 miles, so we have:
Sd*T = (4mph + Sr)*T = 21 mi
When moving upstream, the speed will be:
Su = (4mph - Sr)
and in the same time T as before, she moves 7 miles, so we have the equation:
Su*T = (4mph - Sr)*T = 7 mi
Then we have two equations:
(4mph + Sr)*T = 21 mi
(4mph - Sr)*T = 7 mi
Now we can take the quotient of those two equations and get:
((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7
The time T vanishes, and we can solve it for Sr.
(4mph + Sr)/(4mph - Sr) = 3
4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr
4*Sr = 12mph - 4mph = 8mph
Sr = 8mph/4 = 2mph.
Josslyn is thinking of a number, n and she wants her sister to guess the number. Her first clue is that seven less than six times her number is between negative one and twenty-nine (inclusive). Write a compound inequality that shows the range of number that Josslyn might be thinking of.
Answer:
1<X<=6
Step-by-step explanation:
seven less than six times her number is between negative one and twenty-nine (inclusive).
The above statement can be expressed mathematically thus;
Let the number be x
6x-7= (-1 ,29]
Hence 6x-7 = -1=>6x=6=>x=1 or
6x-7= 29=>6x=36=>x=6
Hence 1<X<=6
Round 8326 to the nearest hundred
Answer:
The answer is 8300.
Step-by-step explanation:
1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.
2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.
3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.
From the mid-1960s to the early 1990s, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in average has a large effect on the tails of the distribution. 0.7% 7% 7.67% 7.6%
Complete Question
From the mid-1960's to the early 1990's, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in average has a large effect on the tails of the distribution.
Estimate the percentage of students scoring over 700 on 1967.
A 0.7%
B 7%
C 7.67%
D 7.6%
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The average SAT score in 1967 is [tex]\= x_1 =543[/tex]
The standard deviation of score in 1967 is [tex]\sigma_ 1= 110[/tex]
The average SAT score in 1994 is [tex]\= x_2 = 499[/tex]
The standard deviation of score in 1967 is [tex]\sigma_ 2 = 110[/tex]
The percentage of students scoring over 700 on 1967 is mathematically represented as
[tex]P(X > 700)[/tex]
Where X is the random variable representing score of student above 700
Now normalizing the above probability we have
[tex]P(X > 700) = P(Z > \frac{700 - \= x_1 }{\sigma } )[/tex]
substituting values
[tex]= P(Z > \frac{700 - \= 543}{110 } )[/tex]
[tex]= P(Z > 1.83 )[/tex]
Form the normalized z table
= 0.076
= 7.6 %
Suppose the labor force is 189 million of a possible 244 million working-age adults. The total number of unemployed is 15 million. What
is the standard unemployment rate?
Answer:
The standard unemployment rate is of 0.0794 = 7.94%.
Step-by-step explanation:
The standard unemployment rate, as a proportion, is the number of unemployed people divided by the size of the labor force.
In this question:
Labor force: 189 million
Number of unemployed people: 15 million
What is the standard unemployment rate?
15/189 = 0.0794
The standard unemployment rate is of 0.0794 = 7.94%.
Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])
Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
Find the mode for the following distribution.
Number Frequency
16
3
20
5
24
9
28
7
32
7
36
5
40
3
24
28
32
28 and 32
Answer:
28 and 32
Step-by-step explanation:
they have the most
Look at the Picture. Look at the Picture.
Answer:
325 square inches
Step-by-step explanation:
Consider the attachment below for further reference. Ideally we would split this figure into parts, and solve as demonstrated by the attachment. I have labeled each rectangle as rectangle 1, rectangle 2, rectangle 3 etc. ;
[tex]Rectangle 1 Area = 17 in * 5 in = 85 square in\\Rectangle 2 Area = ( 17 in - 5 in ) * 14 in = 168 square in,\\Rectangle 3 Area = ( 12 in - 3 in ) * 8 in = 72 square in\\\\Total Area = 85 + 168 + 72 = 325 square inches[/tex]
Hope that helps!
Answer: The answer is 325 inches.
Step-by-step explanation: You can divide the rectangle into multiple parts and find the areas of those parts and add all the areas together at the end
Can someone help me please
Answer:
the triangles are not similar.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 258.7 and a standard deviation of 63.5. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 68.2 and 449.2? b. What is the approximate percentage of women with platelet counts between 195.2 and 322.2?
Answer:
a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
b)[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Step-by-step explanation:
For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:
[tex] \mu = 258.7, \sigma =63.5[/tex]
Part a
We can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\sigma}[/tex]
And we want this probability:
[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
Part b
For this case we want this probability:
[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Determine the next term in the sequence.
14,33,55,83,114....
Answer:
You can't find the next solution without more information.
Step-by-step explanation:
In a class of 30 students, there are four more girls than boys. a)Using x as the number of boys, write down an equation b)Solve the equation and find the number of girls in the class.
easy claps!!
Answer: 30=2x+4 and there are 17 girls in the class.
Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.
It's BASIC prealgebra so you should probably practice bit more with linear equations!
Distance between (-6,8) and (-3,9)
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
substitute
[tex]d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}[/tex]
[tex]\sqrt{10}[/tex]
9. The mean is defined as the
A. number that shows up most often in a data set.
B. average of a data set.
C. middle of the data set.
D. range of the data set.
Answer:
B. Average of the data set
Step-by-step explanation:
The mean is defined as the average of a data set and it's formula is
Mean = [tex]\frac{sum of observations}{number of observations}[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
c
Step-by-step explanation:
when the absolute value of slope gets smaller, the graph of line gets less steeper.
Please answer this correctly without making mistakes
Answer:
746 mi^2
Step-by-step explanation:
The top rectangle has an area of
A = 22*23 =506
The bottom rectangle has an area of
A =10 *24 = 240
Add the areas together
506+ 240 =746
Answer:
746
Step-by-step explanation:
22*23= 506
24*10= 240
506+240= 746
plz mark brainliest
The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 50. A subject earns a score of 155. How many standard deviations from the mean is the value 155
Answer:
The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].
Step-by-step explanation:
The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score: an observation from the normally distributed data that we want standardize using [1].[tex] \\ \mu[/tex] is the population mean.[tex] \\ \sigma[/tex] is the population standard deviation.Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.
For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.
These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.
A subject earns a score of 155. How many standard deviations from the mean is the value 155?
From the question, we know that:
x = 155.[tex] \\ \mu = 155[/tex].[tex] \\ \sigma = 50[/tex].Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{155 - 155}{50}[/tex]
[tex] \\ z = \frac{0}{50}[/tex]
[tex] \\ z = 0[/tex]
As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:
[tex] \\ x = \mu[/tex]
Therefore
[tex] \\ z = 0[/tex]
So, the value 155 is zero standard deviations from the [population] mean.
Assignment
Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.
f(-1) =
f(1) =
f(2)=
>
Answer:
The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.
1. When x=-1, then
f(-1) = 2 * (-1)^3 - 3 * (-1)^2 + 7 = -2 - 3 + 7 = 2.
2. When x=1, then
f(1) = 2 * 1^3 - 3 * 1^2 + 7 = 2 - 3 + 7 = 6.
3. When x=2, then
f(-1) = 2 * 2^3 - 3 * 2^2 + 7 = 16 - 12 + 7 = 11.
Step-by-step explanation:
Answer:
f(−1) =✔ 2
f(1) = ✔ 6
f(2) =✔ 11
Step-by-step explanation:
Which pairs of non-overlapping angles share a ray to make a right angle?
Please Select all that Apply. There are multiple answers. 50 POINTS
∠FGK and ∠FGH Im pretty sure its right
A ray is a half-infinite line. The pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.
What is a ray?A half-infinite line (also known as a half-line) with one of the two points and is commonly used to represent a ray. It is assumed to be infinite.
A straight line has an angle of measurement of 180°. And a 90° angle is made when two lines are perpendicular to each other.
As we can see the line EGH is a straight line, and FG is another line that is perpendicular to line EH, therefore, it will form two angles measuring 90°. These angles will be ∠FGE and ∠FGH.
Hence, the pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.
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Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4. x + 11 = 2 Superscript 4. x + 11 = 16. x = 5. x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2 x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4 x = 5 is a true solution because log Subscript 2 Baseline (16) = 4 x = 5 is a true solution because log Subscript 4 Baseline (16) = 2
Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_2(x+11)=4[/tex]
It can be written as
[tex](x+11)=2^4[/tex] [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]
[tex]x+11=16[/tex]
[tex]x=5[/tex]
Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.
[tex]LHS=\log_2(5+11)[/tex]
[tex]LHS=\log_2(16)[/tex]
[tex]LHS=\log_22^4[/tex]
[tex]LHS=4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]LHS=RHS[/tex]
Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].
Therefore, the correct option is C.
Answer:
C on edge2021
Step-by-step explanation:
The histogram represents the daily low and high temperatures in a city during March. Which comparison of the distributions is true?
A)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.
B)The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.
C)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.
D)The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.
Answer:
ITS C
Step-by-step explanation:
The other answer is wrong, I just tried it.
Answer:
It's C on EDG
Step-by-step explanation:
Die A has 4 red faces and 2 black faces. Die B has 2 red faces and 4 black faces. A coin is flipped once. If it were heads, only die A is used (die B is discarded). If it were tails, only die B is used (die A is discarded). We do not get to know which die was chosen.
a) The first roll of the chosen die gives red. What is the probability that the second roll (with the same die) will be red?
b) The first two rolls of the die were both red. What is the probability that the third roll (with the same die) will be red?
Answer:
a) 5/9
b) 1/3
Step-by-step explanation:
a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)
= 4/6 × 4/6 + 2/6×2/6
= 5/9
b) P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)
= 4/6×4/6×4/6 + 2/6×2/6×2/6
= 1/3
You are given the following data, where X1 (final percentage in history class) and X2 (number of absences) are used to predict Y (standardized history test score in third grade):
Y X1 X2
465 92 2
415 95 2
345 70 3
410 72 3
370 75 4
400 82 0
390 80 1
480 98 0
420 80 2
485 99 0
485 92 6
375 92 6
310 61 5
Determine the following multiple regression values.
Report intercept and slopes for regression equation accurate to 3 decimal places
Intercept: a =
Partial slope X1: b1 =
Partial slope X2: b2 =
Report sum of squares accurate to 3 decimal places:
SSreg = SS
Total =
Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
F-ratio =
P-value =
Report the variance of the residuals accurate to 3 decimal places.
Report the results for the hypothesis test for the significance of the partial slope for number of absences
Answer:
Step-by-step explanation:
Hello!
Given the variables
Y: standardized history test score in third grade.
X₁: final percentage in history class.
X₂: number of absences per student.
Determine the following multiple regression values.
I've estimated the multiple regression equation using statistics software:
^Y= a + b₁X₁ + b₂X₂
a= 118.68
b₁= 3.61
b₂= -3.61
^Y= 118.68 + 3.61X₁ - 3.61X₂
ANOVA Regression model:
Sum of Square:
SS regression: 25653.86
SS Total: 36819.23
F-ratio: 11.49
p-value: 0.0026
Se²= MMError= 1116.54
Hypothesis for the number of absences:
H₀: β₂=0
H₁: β₂≠0
Assuming α:0.05
p-value: 0.4645
The p-value is greater than the significance level, the decision is to not reject the null hypothesis. Then at 5% significance level, there is no evidence to reject the null hypothesis. You can conclude that there is no modification of the test score every time the number of absences increases one unit.
I hope this helps!
The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 21 text messages is taken and results in a sample mean of 30 characters, find a 80% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576
Answer:
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Step-by-step explanation:
We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.
The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.
