Homework 5

Probability Calculation Homework

Supplement – 1: ACT scores of high school seniors. The scores of your state’s high school seniors on the ACT college entrance exam in a recent year had the mean µ = 22.3 and standard deviation σ = 5.2. The distribution of scores is only roughly Normal.

a) What is the approximate probability that a single student randomly chosen from all

those taking the test scores 27 or higher?

b) Now consider an SRS of 16 students who took the test. What are the mean and standard

deviation of the sample mean score x of these 16 students?

c) What is the approximate probability that the mean score of these 16 students is 27 or

higher?

d) Which of your two Normal probability calculations in parts a) and c) is more accurate?

Why?

Supplement – 2: Diabetes during pregnancy. Sheila’s doctor is concerned that she may suffer

from gestational diabetes (high blood glucose levels during pregnancy).There is variation in

both the actual glucose level and in the results of the blood test that measure the level. A

patient is classified as having gestational diabetes if her glucose level is above 140 milligrams

per deciliter (mg/dl) an hour after a sugary drink is ingested. Sheila’s measured glucose level

one hour after ingesting the sugary drink varies according to this Normal distribution with µ =

125 mg/dl and standard deviation σ = 10 mg/dl.

a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed

as having gestational diabetes?

b) If measurements are made instead on three separate days and the mean result is

compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed

as having gestational diabetes?