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 = 58 and estimated standard deviation = 33. 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, x407(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 O The probability distribution of x is approximately normal with -58 and = 16.50. O The probability distribution of x is approximately normal with -58 and -33 O The probability distribution of x is not normal The probability distribution of x is approximately normal with --58 and-23.33. What is the probability that x

Explanation / Answer

a) P(X<40)=P(Z<(40-58)/33)=P(Z<-0.5455)=0.2927

b) approximately normal wth mean =58 and std deviation =23.33

P(Xbar<40)=P(Z<-0.7714) =0.2202

c)

here std error =33/(3)1/2 =19.053

P(Xbar<40)=P(Z<(40-58)/19.053)=P(Z<-0.9448)=0.1724

d)

std error =33/(5)1/2 =14.758

P(Xbar<40)=P(Z<(40-58)/14.758)=P(Z<-1.2197)=0.1113

e) Yes

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