SOLUTION: Assume that the population of heights of female college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 2.75 inches. A random sa

Question 309706: Assume that the population of heights of female college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 2.75 inches. A random sample of 16 heights is obtained. Show all work.

(A) Find the proportion of female college students whose height is greater than 69 inches.

(B) Find the mean and standard error of the distribution

(C) Find
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 68 inches and standard deviation s of 2.75 inches.
A random sample of 16 heights is obtained. Show all work.
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Note: The mean of all samples of size 16 is 68
The std of all samples of size 16 is 2.75/sqrt(16) = 2.75/4
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(A) Find the proportion of female college students whose height is greater than 69 inches.
Note: This is not a sample of size 16 so the std is 2.75.
z(69)= (69-68)/2.75 = 0.3636
P(x> 69) = P(z> 0.3636) = 0.3581
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(B) Find the mean and standard error of the distribution
Note: This seems to refer to the samples of size 16.
mean = 2.75
standard error = 2.75/sqrt(16) = 0.6875
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(C) Find P(x >= 69)
If this refers to the distribution of sample means,
z(69) = (69-68)/[2.75/sqrt(15)] = 1.4545
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P(x-bar >= 69) = P(z >= 1.4545) = 0.0729
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Cheers,
Stan H.
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Cheers,
Stan H.

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