Question 230644
Assume that the population of heights of male students is approximately normally distributed with mean of 68 inches and Standard deviation of 3.75 inches. A random sample of 16 heights is obtained. Show all work
z(70) = (70-68)/3.75 = 8/15
 
A. Find the proportion of male students whose height is greater than 70 inches.
P(x > 70) = P(z > 8/15) = 0.2969
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B. Find the mean and Standard deviation error of the x distribution
If you mean the x-bar distribution, the mean of the sample means = 68
and the std of the sample means is 3.75/sqrt(16) = 3.75/4 = 0.9375
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C. Find p(x-bar > 70)
z(70) = (70-68)/0.9375 = 2.133333...
P(x-bar > 70) = P(z > 2.133333..) = 0.1645
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Cheers,
Stan H.