The heights of a pediatrician’s three-year-old females are approximately normally distributed, with mean 38.72 inches and standard deviation 3.17 inches. Find the height of a three-year-old female at the 20th percentile.

By-Hand Approach

Step 1 Draw a normal curve and shade the desired area.
Step 2 Use Table V to find the z-score that corresponds to the shaded area.
Step 3 Obtain the normal value from the formula x = μ + zσ.*

Technology Approach

Step 1 Draw a normal curve and shade the desired area.

Step 2 Use a statistical spreadsheet or calculator with advanced statistical features to find the score. The steps for determining the value of a normal random variable, given an area, using the TI-83/84 Plus graphing