SOLUTION: Please help. I have tried to find similar problems and work this out but I have only confused myself more. Thank you, it is the only one I haven't been able to answer and it is d

Question 720784: Please help. I have tried to find similar problems and work this out but I have only confused myself more. Thank you, it is the only one I haven't been able to answer and it is due 3/2/13.
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)
(B) Find the mean and standard error of the x-bar distribution
(C) Find P(x-bar>68.75)
(D) Why is the formula required to solve (A) different than (C)?

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 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
------------------------------------
(B) Find the mean and standard error of the x-bar distribution
mean = 69.66 ; std = 6.08/sqrt(84) = 0.6634
------------------------------------

(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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