Question

the heights of south african men are normally distributed with mean of 69 inches and standard deviation of 4 inches. If random sample of 3 men were selected at random, what is probability all three of their heights are greater than 72 inches?

Answer 1

The z-score for 72 inches is given by
\[z=\frac{72-69}{4}=0.75\]
Reference to a standard normal distribution table shows that the probability of height being less than 72 inches is 0.7734. Therefore the probability of height being greater than 72 inches is 1.000 - 0.7734 = 0.2266
Therefore the probability of all three randomly selected men having heights greater than 72 inches is
\[0.2266^{3}=you\ can\ calculate\]