Let x be a random variable that represents the level ofglucose in the blood (milligrams per deciliter of blood) after a 12hour fast. Assume that for people under 50 years old, xhas a distribution that is approximately normal, with meanμ = 65 and estimated standard deviation σ = 31. Atest result x < 40 is an indication of severe excessinsulin, and medication is usually prescribed.
(a) What is the probability that, on a single test, x< 40? (Round your answer to four decimal places.)
(b) Suppose a doctor uses the average x for two teststaken about a week apart. What can we say about the probabilitydistribution of x? Hint: See Theorem 6.1.
The probability distribution of x is not normal.Theprobability distribution of x is approximately normal withμx = 65 andσx = 21.92.    Theprobability distribution of x is approximately normal withμx = 65 andσx = 31.The probability distributionof x is approximately normal withμx = 65 andσx = 15.50.
What is the probability that x < 40? (Round your answerto four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart.(Round your answer to four decimal places.)
(d) Repeat part (b) for n = 5 tests taken a week apart.(Round your answer to four decimal places.)
(e) Compare your answers to parts (a), (b), (c), and (d). Did theprobabilities decrease as n increased?
YesNo   Â
Explain what this might imply if you were a doctor or a nurse.
The more tests a patient completes, the weaker is the evidencefor excess insulin.The more tests a patient completes, the strongeris the evidence for excess insulin.    The moretests a patient completes, the weaker is the evidence for lack ofinsulin.The more tests a patient completes, the stronger is theevidence for lack of insulin.
