Medical: Blood Glucose Let x be a random variable that represents the level of glucose in the blood

(milligrams per deciliter of blood) after a 12-hour fast.

Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean m 5 85 and estimated standard deviation s 5 25

(based on information from Diagnostic Tests with Nursing Applications, edited by S. Loeb, Springhouse).

A test result x , 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x , 40?

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x ? Hint: See Theorem 6.1. What is the probability that x , 40?

(c) Repeat part

(b) for n 5 3 tests taken a week apart.

(d) Repeat part

(b) for n 5 5 tests taken a week apart.

(e) Interpretation Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? Explain what this might imply if you were a doctor or a nurse. If a patient had a test result of x , 40 based on five tests, explain why either you are looking at an extremely rare event or (more likely) the person has a case of excess insulin.AppendixLO1