Probability & Statistics NAME: ______________________________________

Section 3.4 Worksheet

Please do all work on a separate sheet of paper.

Include a sketch for each problem.

(1) High IQ Scores Scores on the Wechsler Adult Intelligence Scale for 20- to 34-year-olds are approximately

Normally distributed with mean 110 and standard deviation 25. How high must a person score to be in the top

25% of all scores?

(2) Low-Birth-Weight Babies Researchers in Norway analyzed data on the birth weights of 400,000 newborns over

a 6-year period. The distribution of birth weight is approximately Normal with a mean of 3,668 grams and a

standard deviation of 511 grams. Below what birth weight do 80% of all babies weigh?

(3) Gestation Period The length of human pregnancies from conception to birth varies according to a distribution

that is approximately normal with a mean of 266 days and a standard deviation of 16 days. How long do the

longest 10% of pregnancies last? (In other words, below what number of days do 90% of all pregnancies last?)

(4) Helmet Sizes The army reports that the distribution of head circumferences among soldiers is approximately

normal with a mean of 22.8 inches and a standard deviation of 1.1 inches. Helmets are mass-produced for all

except the smallest 5% and the largest 5% of head sizes. Soldiers in the smallest or largest 5% get custom-made

helmets.

(a) What head circumferences would place a soldier in the smallest 5%?

(b) What head circumferences would place a soldier in the largest 5% (meaning that 95% of all soldiers’

head sizes were smaller than theirs)?

Section 3.4 Worksheet

KEY

(1) x ≈ 126.75

(2) x ≈ 4,097.24 grams

(3) x ≈ 286.48 days

(4) (a) x ≈ 20.996” or less

(b) x ≈ 22.604” or more