Question 757283: The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 40 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 40?
Shape is normal, mean of the sample means=67 mph, std of the sample means of the size 40 6/ (sqrt
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 65 and 68 miles per hour?
D) What is the probability that the sample mean will be less than 66 miles per hour?
2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 200 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 200?
B) What is the probability that the sample proportion will fall within 0.02 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 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 40 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 40?
Shape is normal, mean of the sample means=67 mph, std of the sample means of the size 6/sqrt(40)
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B) What is the probability that the sample mean will be 69 miles per hour or more?
z(69) = (69-67)/[6/sqrt(40)]= 2.1082
P(x-bar >= 69) = P(z >= 2.1082) = 0.0175
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C) What is the probability that the sample mean will be between 65 and 68 miles per hour?
Find the z-value of 65 and of 68
Find the probability z is between those z-values.
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D) What is the probability that the sample mean will be less than 66 miles per hour?
Use the same process as with "a" and "b".
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2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 200 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 200?
normal; mean = 0.35 ; std = sqrt[0.35*0.65/200] = 0.0337
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B) What is the probability that the sample proportion will fall within 0.02 of the population proportion?
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Find the z value that is 2% above the mean.
invNorm(0.52) = 0.0502
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So the z-values that are 2% above and below the mean are +-0.0502
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Use x = z*s+u to find the corresponding proportions:
x = 0.0502*0.03370 + 0.35 = 0.3517
and
x = -0.0502*0.03370 + 0.35 = 0.3483
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Cheers,
Stan H.
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