Let x be a random variable that represents the level of glucose in the blood (mi

Question

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 = 93 and estimated standard deviation = 31. 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.

The probability distribution of x is approximately normal with x = 93 and x = 21.92.The probability distribution of x is approximately normal with x = 93 and x = 31.     The probability distribution of x is not normal.The probability distribution of x is approximately normal with x = 93 and x = 15.50.

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

Explanation / Answer

a)P(X<40) =P(Z<(40-93)/31) =P(Z<-1.7097)=0.0437

b)The probability distribution of x is approximately normal with x = 93 and x = 21.92

P(X<40)=0.0078

c) x =17.8979

P(X<40)=0.0015

d) x =13.8636

P(X<40)=0.00007

e)Yes

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