# Let x be a random variable that represents the level of glucose in

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 *μ* = 54 and estimated standard deviation *σ* = 43. A test result *x* < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) 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.The probability distribution of *x* is approximately normal with *μx* = 54 and *σx* = 30.41.

b)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.)

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