SOLUTION: Assume that the population of heights of male college students is approximately normally distributed with mean m of 69.34 inches and standard deviation s of 3.58 inches. A random s

Question 701175: Assume that the population of heights of male college students is approximately normally distributed with mean m of 69.34 inches and standard deviation s of 3.58 inches. A random sample of 76 heights is obtained.
(A) Find the mean and standard error of the X distribution
(B) Find Px>69.25
Can some one walk me through this
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume that the population of heights of male college students is approximately normally distributed with mean m of 69.34 inches and standard deviation s of 3.58 inches. A random sample of 76 heights is obtained.
(A) Find the mean and standard error of the X distribution
Note: I assume by "x" distribution you mean the distribution of the
sample means.
Using the Central Limit Theorem,
The mean of the sample means = mean of the population = 69.34 inches
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The std of the sample means = (std of pop)/sqrt(sample size) = 3.58/sqrt(76)
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(B) Find P(x>69.25)
z(69.25) = (69.25-69.34)/[3.58/sqrt(76)] = -0.2192
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P(x > 69.25) = P(z > -0.2192) = 0.5867
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Cheers,
Stan H.
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