Question 720784
Assume that the population of heights of male college students is approximately normally distributed with mean u of 69.66 inches and standard deviation o of 6.08 inches. A random sample of 84 heights is obtained. Show all work. 
(A) Find P(x > 68.75)
z(68.75) = (68.75-69.66)/6.08] = -0.1497
P(x > 68.75) = P(z > -0.1497) = normalcdf(-0.1497,100) = 0.5595
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(B) Find the mean and standard error of the x-bar distribution
mean = 69.66 ; std = 6.08/sqrt(84) = 0.6634
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(C) Find P(x-bar>68.75)
P(x-bar > 68.75)
z(68.75) = (68.75-69.66)/[6.08/sqrt(84)] = -1.3718
P(x-bar) > 68.75) = P(z > -1.3718) = normalcdf(-1.3718,100) = 0.9149

(D) Why is the formula required to solve (A) different than (C)?
The Central Limit Theorem explains that.
Cheers,
Stan H.
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