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 = 71 and estimated standard deviation = 39. 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? (Round your answer to four decimal places.)

(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.
a. The probability distribution of x is approximately normal with x = 71 and x = 27.58.
b. The probability distribution of x is approximately normal with x = 71 and x = 39.
c. The probability distribution of x is approximately normal with x = 71 and x = 19.50.
d. The probability distribution of x is not normal.

What is the probability that x < 40? (Round your answer to 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 the probabilities decrease as n increased?
Yes
No

Explain what this might imply if you were a doctor or a nurse.
a. The more tests a patient completes, the stronger is the evidence for lack of insulin.
b. The more tests a patient completes, the stronger is the evidence for excess insulin.
c. The more tests a patient completes, the weaker is the evidence for lack of insulin.
d. The more tests a patient completes, the weaker is the evidence for excess insulin.