Question

The heights of adult males are known to be normally distributed with a mean of 70 inches and a standard deviation of 2 inches.

a) Find the probability that a randomly selected adult male will be taller than 75 inches?

(b) If three adult males are picked at random, find the probability that at least one of the males is taller than 75 inches.

Answer 1

We are given the heights distribution here as:

a) The probability here is computed as:
P(X > 75)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0062 is the required probability here.

b) Probability that at least one of the three males selected is talled than 75 inches is computed here as:

= 1 - Probability that none of them are taller than 75 inches

= 1 - (1 - 0.0062)3 = 0.0185

Therefore 0.0185 is the required probability here.