Question

The height, X , of American teens is distributed normally with a mean u = 65.5 inches and the standard deviation o = 2.5 inches. Find the probability of each of the following events.

a. ? < 67 inches

b. 64 < X < 67 inches

Answer 1

Given that

Standardizing the variable,

a. P(X < 67)

The probability is nothing but the area of the standard normal curve corresponding to the Z score.Standard normal table gives the area to the left of the Z score and hence, left tail probabilities.

Hence, P(X < 67) = 0.72575

b. P(64 < X < 67)

............(Since, normal tables gives the area to the left of the Z score)

= 0.72575 - 0.27425

= 0.45150

Hence, P(64 < X < 67) = 0.45150