The lengths of infants at birth in a certain hospital are normally distributed with a mean of 18 inches and a standard deviation of 2.2 inches. find the probability that an infant selected at random from this hospital measures between 16 and 21 inches.

Mean, m = 18 in

Standard deviation, SD = 2.2 in

Range: 16 ≤ X ≤ 21 in

Calculating Z value,

Z = (X-m) / SD

Then,

Z1 = (16-18) / 2.2 ≈ - 0.91

Z2 = (21-18) / 2.2 ≈ 1.36

From Z table, and at Z1 = - 0.91, and Z2 = 1.36;

P (16) = 0.1814

P (21) = 0.9131

Therefore,

P (16≤X≤21) = 0.9131 - 0.1814 = 0.7317

The probability that a child selected randomly measures between 16 and 21 in is 0.7317.