Question 330976
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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