Suppose that the height of female students at a large university is normally distributed with a mean of 64 inches and a standard deviation of 2.8 inches. if 10 samples consisting of 50 students each are obtained, what is the probability that the mean of any one of these 10 samples is greater than 65 inches?

To solve the question we proceed as follows:
z-score is given by:
z=(x-μ)/σ
where:
μ- mean
σ-standard deviation

The z-score of our information will be:
z=(65-64)/2.8
z=0.3571
thus the probability associated with this z-score is:
P(X≤x)=0.6404

Thus the probability that the mean of any one of these 10 samples is greater than 65 inches will be:
P(X≥x)=1-P(X≤x)
=1-0.6404
=0.3596