Chapter 17, Problem 56E

Exercises 53 through 56 refer to the distribution of weights for infants by age and gender. In all cases you can assume that the weight distribution is approximately normal. The data for these exercises are taken from the 2000 clinical growth charts by the Centers of Disease Control and Prevention (CDC) (www.cdc.gov/growthcharts/clinical_charts.htm).

The distribution of weights for 12-month-old baby boys has mean $\mu =10.5\text{ kg}$ and standard deviation $\sigma =1.2\text{ kg}$.

a. Suppose that a 12-month-old boy weighs 11.3 kg.

Approximately what weight percentile is he in?

b. Suppose that a 12-month-old boy weighs 8.1 kg.

Approximately what weight percentile is he in?

c. Suppose that a 12-month-old boy is in the ${84}^{th}$ percentile in weight. Estimate his weight.