Question 330976: 1. 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 50 cars is to be selected for a speed study.
A) What is the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 50?
B) What is the probability that a 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?
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 50 cars is to be selected for a speed study.
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A) What is the shape, mean, and standard deviation of the sampling distribution
Shape is normal;
mean of the sample means = 67 mph ;
std of the sample means = 6/(sqrt(50)) = (6/5)sqrt(2)
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B) What is the probability that a sample mean will be 69 miles per hour or more?
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t(69) = (69-67)/[6/sqrt(50)] = 2.357
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P(xbar >= 69) = P(t >= 2.357 when df = 49) = 0.0112
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C) What is the probability that the sample mean will be between 65 and 68 miles per hour?
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P(65 < xbar < 68) = P(-2.357 < t < 1.1785 when df = 49) = 0.8666
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Cheers,
Stan H.
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