Answer:
Between 0.01 and 0.20
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 500, p = 0.05[/tex]
So
[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]
Find the probability of winning at least 30 times.
Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)[/tex]. So this is 1 subtracted by the pvalue of Z when X = 29.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29.5 - 25}{4.8734}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a pvalue of 0.8212
1 - 0.8212 = 0.1788
So the correct option is:
Between 0.01 and 0.20
A factory received a shipment of 10 generators, and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
Answer:
A) 0.026
B) 0.130
Step-by-step explanation:
Complete Question
A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.
(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.
Solution
A) This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 4
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.
B) n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 0
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.
Hope this Helps!!!
The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the length of the shorter leg of the right triangle.
Answer:
8 units.
Step-by-step explanation:
The smaller of the right triangles formed is similar to the whole triangle so
4/x = x/16 where x = the shorter leg
x^2 = 64
x = 8.
The length of the shorter leg of the right triangle is 3 units.
Let's denote the length of the shorter leg of the right triangle as "x." Since the altitude drawn to the hypotenuse divides it into segments of lengths 4 and 12, we can set up a proportion between the two triangles formed.
According to the similarity of triangles, the length of the shorter leg to the length of the segment of the hypotenuse it divides is the same as the length of the longer leg to the length of the other segment of the hypotenuse.
So, we can set up the proportion:
x / 4 = 12 / (hypotenuse length).
Now, we know that the hypotenuse length is equal to the sum of the two segments (4 + 12 = 16). We can substitute it into the proportion:
x / 4 = 12 / 16.
Now, cross-multiply and solve for x:
16x = 4 * 12,
16x = 48,
x = 48 / 16,
x = 3.
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if two adjecent complentary angles are congruent then what is the measure of each angle?
A boy is playing a ball in a garden surrounded by a wall 2.5 m high and kicks the ball vertically up from a height of 0.4 m with a speed of 14 m/s . For how long is the ball above the height of the wall.
Answer:
2.5 sec
Step-by-step explanation:
Height of wall = 2.5 m
initial speed of ball = 14 m/s
height from which ball is kicked = 0.4 m
we calculate the speed of the ball at the height that matches the wall first
height that matches wall = 2.5 - 0.4 = 2.1 m
using = + 2as
where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)
= + 2(-9.81 x 2.1)
= 196 - 41.202
= 154.8
v = = 12.44 m/s
this is the velocity of the ball at exactly the point where the wall ends.
At the maximum height, the speed of the ball becomes zero
therefore,
u = 12.44 m/s
v = 0 m/s
a = -9.81 m/s^2
t = ?
using V = U + at
0 = 12.44 - 9.81t
-12.44 = -9.81
t = -12.44/-9.81
t = 1.27 s
the maximum height the ball reaches will be gotten with
= + 2as
a = -9.81 m/s^2
0 = + 2(-9.81s)
0 = 196 - 19.62s
s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.
height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m
we calculate for the time taken for the ball to travel down this height
a = 9.81 m/s^2 (positive in downwards movement)
u = 0
s = 7.49 m
using s = ut + a
7.49 = (0 x t) + (9.81 x )
7.49 = 0 + 4.9
= 7.49/4.9 = 1.53
t = = 1.23 sec
Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec
On a piece of paper, graph fx) = 2• (0.5)*. Then determine which answer choice matches the graph you drew.
Answer:
Graph A
Step-by-step explanation:
The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.
I hope this helps :))
The graph A is correct.
What is a graph?A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.
The equation is,
[tex]y=2(0.5)^{x}[/tex]
Plotting the graph, we get,
Option A
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Write an equation in point-slope form for the line that has the given slope, m, and
that passes through the given point and graph the line.
m = -2; (-1,4)
Step-by-step explanation:
work is shown and pictured
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
Answer:
V ≈ 382 inches ³
Step-by-step explanation:
V = 4/3πr³
V = 4/3(3.14)(4.5)³
V = 1145.11/3
V = 381.7
V ≈ 382 inches ³
What translation was used to ABCD to produce A’ B’C’D’
You play a game that requires rolling a six sided die then randomly choosing a card from a deck containg 8 red cards ,6 blue cards and 8 yellow cards whats the probability that younroll a 3 on the due and choose a red card
Answer:
2/33
Step-by-step explanation:
Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)
Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)
8/22 = 4/11
Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11
= 4/66
= 2/33
Ronnie invested $1500 in an account that earns 3.5% interest, compounded annually. The formula for compound interest is A(t) = P{(1 + i)^t}A(t)=P(1+i) t . How much did Ronnie have in the account after 4 years?
Answer:
BStep-by-step explanation:
A= New amount
P= Principal or Original amount which is £1500
I= Interest
t= time period
3.5% as a decimal is 3.5÷100=0.035
time period= 4 years
so 1500(1+0.035)^4 = B
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were:
y = a + bx
a = -0.762
b = 0.119
r2 = 0.8649
r = 0.93
A) Write the equation of the Least Squares Regression line of the form y = + x
B) If a country increases its life expectancy, the happiness index will increase or decrease?
C) If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change?
D) Use the regression line to predict the happiness index of a country with a life expectancy of 67 years.
Answer:
(A) [tex]y=-0.762+0.119x[/tex]
(B) If a country increases its life expectancy, the happiness index will increase.
(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
Step-by-step explanation:
A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).
The output of the regression analysis are as follows:
a = -0.762
b = 0.119
r² = 0.8649
r = 0.93
(A)
The equation of the Least Squares Regression line of the form y = _ + _ x is:
[tex]y=-0.762+0.119x[/tex]
(B)
The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.
The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.
Thus, if a country increases its life expectancy, the happiness index will increase.
(C)
Compute the value of y for x = x + 3.5 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]
Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D)
Compute the value of y for x = 67 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]
Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
What would be the approximate 95% confidence interval for the mean number of ounces of catchup bottle in the sample
Answer:
The 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Step-by-step explanation:
The complete question is:
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.8 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?
Solution:
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\bar x=24\\\sigma=0.8\\n=49\\\text{Confidence Level}=95\%[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the 95% confidence interval for the mean number of ounces of ketchup per bottle as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]=24\pm1.96\cdot \frac{0.80}{\sqrt{49}}\\\\=24\pm 0.224\\\\=(23.776, 24.224)\\\\\approx (23.8, 24.2)[/tex]
Thus, the 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Which expression best represents the situation?
Select the expression that best matches the scenario.
O4 + x + 3
4(x + 3)
4.3
4x + 3
Tyson bought a burger for himself and
each of his 3 friends. He left a tip of $3.
Which expression could represent
the amount of money Tyson spent?
Explain your thinking.
Help plz
Answer:509
Step-by-step explanation:600
Solving an Equation Using Algebra Tiles
Arrange the tiles on both boards to find the value of x.
What is the value for x when solving the equation
-x+ (-1) = 3x + (-5) using algebra tiles?
O x= -1
O x= 1
OX= 2
O x=3
Board sum: (-x) + (-1) = 3x + (-5)
Reset
The tiles are ready for moving
Done
Intro
Answer:
[tex]\boxed{ \ x = 1 \ }[/tex]
Step-by-step explanation:
hi,
-x+(-1)=3x+(-5)
<=>
-x-1=3x-5
<=>
3x+x = -1+5 = 4
<=>
4x=4
<=>
x=1
thanks
The value of x when solving the equation -x+ (-1) = 3x + (-5) is 1
Algebraic expression:Algebraic expression is a union of terms by the operations such as addition, subtraction, multiplication, division, etc
-x + (-1) = 3x + (-5)
The value of x can be found as follows:
-x + (-1) = 3x + (-5)
Let's open the parenthesis, Therefore,
-x - 1 = 3x - 5
-x - 3x = -5 + 1
-4x = -4
divide both sides by -4
-4x / -4 = -4 / -4
x = 1
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY.
Answer:
B, E
Step-by-step explanation:
A line has a negative slope when it decreases going left to right.
As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).
Answer:
B & E
Step-by-step explanation:
A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 8 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store.
Answer: 0.401294
Step-by-step explanation:
z=x-μ/σ
z=20-22/8
z=-0.25
the probability for this z-score is 0.401294.
Display the values of the function in two ways: (a) by sketching the surface zequals=f (x comma y )f(x,y) and (b) by drawing an assortment of level curves in the function's domain. Label each level curve with its function value.
Answer:
(1) f(x,y) = 1-|x|-|y|
(a) 3d figure attached
(b) 2d figure attached
(2) f(x,y) = 6-2x-3y
(a) 3d figure attached
(b) 2d figure attached
Step-by-step explanation:
The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem
(1) f(x,y) = 1-|x|-|y|
(2) f(x,y) = 6-2x-3y
All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches
NEED GEOMETRY HELP ASAP PLEASE (11 POINTS)
Answer:
d = 2[tex]\sqrt{17}[/tex]
Step-by-step explanation:
P1 (-5, 4) P2 (-3, -4)
Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Plug in the values and simplify
d = [tex]\sqrt{(-3 + 5)^{2} + (-4 -4)^{2} }[/tex]
d = [tex]\sqrt{(2)^{2} + (-8)^{2} }[/tex]
d = [tex]\sqrt{4 + 64 }[/tex]
d = [tex]\sqrt{68}[/tex]
d = 2[tex]\sqrt{17}[/tex]
I hope this helps :)
please help i dont know how to answer this
Answer:
The answer is s / s + 3
Step-by-step explanation:
I applied the fraction rule a/b divided by c/d = a/b times c/d
Please mark BRAINLIEST!
What is the measure of
55°
The sum or measures of interior angle in a triangle is 180°.
Angle A, 35° + Angle C, 90° =125°
Angle B= 180°-125°=55°[angle B]
en una division el 42 es el cociente el divisor 12 y el dividendo 513 ¿Cual es el resto?
Answer:
El resto es 9.
Step-by-step explanation:
En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.
Please answer this correctly
Answer:
21-25 = 4
26-30 = 3
Step-by-step explanation:
16-20 (4)= 17 17 17 18
21-25 (4)= 21 22 24 25
26-30 (3)= 26 27
30
31-35 (3)= 32 35 35
36-40 (5)= 36 37 37 38 39
41-45 (2)= 41 42
uppose that the length of 20 years worth of baseball games has been investigated, and that it has been found that the average (mean) length of a game is 165 minutes and the standard deviation is 30 minutes. What is the probability that a randomly selected game will last between 120 and 210 minutes
Answer:
P(120< x < 210) = 0.8664
Step-by-step explanation:
given data
time length = 20 year
average mean time μ = 165 min
standard deviation σ = 30 min
randomly selected game between = 120 and 210 minute
solution
so here probability between 120 and 210 will be
P(120< x < 210) = [tex]P(\frac{120-165}{30}< \frac{x-\mu }{\sigma } <\frac{210-165}{30})[/tex]
P(120< x < 210) = [tex]P(\frac{-45}{30}< \frac{x-\mu }{\sigma } <\frac{45}{30})[/tex]
P(120< x < 210) = P(-1.5< Z < 1.5)
P(120< x < 210) = P(Z< 1.5) - P(Z< -1.5)
now we will use here this function in excel function
=NORMSDIST(z)
=NORMSDIST(-1.5)
P(120< x < 210) = 0.9332 - 0.0668
P(120< x < 210) = 0.8664
There are two fields whose total area is 56 square yards. One field produces grain at the rateof34bushel per square yard; the other field produces grain at the rate of23bushel per squareyard. If the total yield is 40 bushels, what is the size of each field
Answer:
the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
Step-by-step explanation:
With the statement we can make a system of 2x2 equations, where:
"x" is the area of the first field
"y" is the area of the second field
However,
x + y = 56 => x = 56 - y
3/4 * x + 2/3 * y = 40
replacing we have:
3/4 * (56 - y) + 2/3 * y = 40
42 - 3/4 * y + 2/3 * y = 40
-0.0833 * y = 40 - 42
y = -2 / -0.0833
y = 24
now for x:
x = 56 - 24
x = 32
This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
help help help help help
Answer:
See below
Step-by-step explanation:
a.
[tex]\dfrac{10}{4}=\dfrac{5(2)}{2(2)}=\dfrac{5}{2}[/tex]
b.
[tex]\dfrac{20}{15}=\dfrac{4(5)}{3(5)}=\dfrac{4}{3}[/tex]
c.
[tex]\dfrac{-24}{42}=\dfrac{-4(6)}{7(6)}=\dfrac{-4}{7}[/tex]
d.
[tex]\dfrac{-18}{-14}=\dfrac{-2(9)}{-2(7)}=\dfrac{9}{7}[/tex]
Hope this helps!
Solve for n:
6 - 24n = 3n + 6
Answer:
0
Step-by-step explanation:
6-24n=3n+6
Add 24n to both sides of the equation:
6=27n+6
Subtract 6 from both sides:
27n=0
Therefore, n=0.
Hope this helps!
Simplify
20x over 70x
Answer:
The answer is 2/7.
Step-by-step explanation:
You have to cut out the common terms :
[tex] \frac{20x}{70x} [/tex]
[tex] \frac{20}{70} [/tex]
[tex] \frac{2}{7} [/tex]
Please help me answer the question, answer problem 1 and 2
please see the attached picture for full solution
Hope it helps...
Good luck on your assignment,
The graph of Ax), shown below, resembles the graph of G(X) = x, but it has
been stretched and shifted. Which of the following could be the equation of
Fx)?
Answer:
sorry'but I don't know the answer
A toy manufacturer wants to know how many new toys children buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.8 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 80% level of confidence
Answer:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]
So the answer for this case would be n=369 rounded up to the nearest integer
Step-by-step explanation:
We know the following info given:
[tex] \sigma = 1.8[/tex] represent the standard deviation
[tex]\mu = 5.8[/tex] the true mean that she believes
[tex] ME = 0.12[/tex] represent the margin of error
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+0.12 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 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]
So the answer for this case would be n=369 rounded up to the nearest integer
