Question

Suppose the heights of men are normally distributed with mean, μ = 69.5 inches, and standard deviation , σ = 4 inches. suppose admission to a summer basketball camp requires that a camp participant must be in the top 40 % of men's heights, what is the minimum height that a camp participant can have in order to meet the camp's height admission requirement?

Answer 1

To evaluate for the height we use the z-score formula given by:
z=(x-mu)/sig
where:
mean=mu=69.5 inches
sig=standard deviation=4
Given that:
P(x>X)=0.40
then 
P(x<X)=1-0.40=0.60
thus the z-value corresponding to this is:
P(z<Z)=0.25
hence:
0.25=(x-69.5)/4
solving for x we get:
1=x-69.5
x=1+69.5
x=70.5
thus the minimum height should be 70.5 inches