Question 916881: 1. The speed of automobiles on a section of I-95 is normally distributed with a population mean of 65 miles per hour and a population standard deviation of 8 miles per hour. A random sample of 30 cars is to be selected for a speed study.
A) What are the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 30?
B) What is the probability that the sample mean will be 69 miles per hour or more?
C) What is the probability that the sample mean will be between 62 and 68 miles per hour? By how much would your answer change if the sample size had been 60?
D) What is the probability that the sample mean will be less than 63 miles per hour?
2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 500 adults is to be selected to test this claim.
A) What are the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 500?
B) What is the probability that the sample proportion will fall within 0.03 of the population proportion?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The speed of automobiles on a section of I-95 is normally distributed with a population mean of 65 miles per hour and a population standard deviation of 8 miles per hour. A random sample of 30 cars is to be selected for a speed study.
A) What are the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 30?
shape:: normal
mean:: 65 mph
std:: 8/sqrt(30)
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B) What is the probability that the sample mean will be 69 miles per hour or more?
z(69) = (69-65)/(8/sqrt(30)) = 2.74
P(x >= 69) = P(z > 2.74) = normalcdf(2.74,100) = 0.003
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C) What is the probability that the sample mean will be between 62 and 68 miles per hour?
Find the z-values for 62 and 68
Then find the probability between those z-values.
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By how much would your answer change if the sample size had been 60?
Try it.
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D) What is the probability that the sample mean will be less than 63 miles per hour?
Find the z-value ; Find prob z is less than that z-value.
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2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 500 adults is to be selected to test this claim.
A) What are the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 500?
shape:: normal
mean:: 0.35
std:: sqrt(pq/n) = sqrt(.5^2/500) = 0.0224
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B) What is the probability that the sample proportion will fall within 0.03 of the population proportion?
Can you handle that?
Cheers,
Stan H.
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