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.
---
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 
---------- 

(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
--------------------------------------

(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
=============================================
(C) Find P(x >= 69)
If this refers to the distribution of sample means,
z(69) = (69-68)/[2.75/sqrt(15)] = 1.4545
---
P(x-bar >= 69) = P(z >= 1.4545) = 0.0729
=====================================================
Cheers,
Stan H.
================================================= 

=============================================
Cheers,
Stan H.