Question 459584: Assume that the population of heights of female college students is approximately normally distributed with mean m of 67.16 inches and standard deviation s of 4.82 inches. A random sample of 92 heights is obtained. Show all work.
(A) Find the mean and standard error of the x distribution
(B) Find P(x > 67.75)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume that the population of heights of female college students is approximately normally distributed with mean m of 67.16 inches and standard deviation s of 4.82 inches. A random sample of 92 heights is obtained. Show all work.
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I'm going to assume you mean the x-bar distribution, which
is the probability distribution of the sample means.
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(A) Find the mean and standard error of the x distribution
u(x-bar) = 67.16
s(x-bar) = 4.82/sqrt(92)
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(B) Find P(x-bar > 67.75)
t(67.75) = (67.75-67.16)/[4.82/sqrt(92)] = 1.17
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P(x-bar > 67.75) P(t > 1.17 when df = 91) = tcdf(1.17,100,91) = 0.12
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cheers,
Stan H.
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