The chest measurements for 5738 Scottish militiamen in the early 19th century are given below. Chest sizes are measured in inches, and each observation reports the number of soldiers with that chest size.

Notice the approximate normality of the histogram of the 5738 chest measurements.

a. The mean of this distribution is = 39.83 and the standard deviation is s = 2.05. What is the 95th percentile of this distribution based on a normal curve with µ = 39.83 and σ = 2.05?
b. Find the empirical estimate of the 95th percentile and compare with your answer in part a. c. Find the 90th percentile of this distribution based on a normal curve with µ = 39.83 and σ = 2.05. What is the value of the empirical 90th percentile? How does it compare with the value assuming normality?

Transcribed Image Text:

Count Chest 18 34 81 35 185 36 420 37 749 38 1073 39 1079 40 Count Chest 934 41 658 42 370 43 92 44 50 45 21 46 4 47 1 48 Histogram of Chest Measurements 1200 1000 800 - 600- 400- 200- 33 34 3S 36 37 38 39 40 41 42 43 44 45 46 47 48 Chest Measurement in Inches)