20. Normal Distribution? The chest measurements for 5738 Scottish militiamen in the early 19th century are given here.16 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 x 539.83 and the standard deviation is s52.05. What is the 95th percentile of this distribution based on a normal curve with m 539.83 and s 52.05?

b. Find the empirical estimate of the 95th percentile and compare with your answer in part a.
(hint: The 95th percentile will be in position .95(n 1 1)5.95 × 573955452.05 from the left tail of the distribution or in position 573825452.055285.95 from the right tail of the distribution.)

c. Find the 90th percentile of this distribution based on a normal curve with m 539.83 and s 52.05. What is the value of the empirical 90th percentile? How does it compare with the value assuming normality?

Transcribed Image Text:

Count Chest Count Chest 3 33 934 41 18 34 658 42 81 35 370 43 185 36 92 44 420 37 50 45 749 38 21 46 1073 39 4 47 1079 40 - 1 48