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 = 81 and estimated standard deviation = 24. 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 okRint. See Theorem 5.. The probability distribution of x is approximately normal with = 81 and = 24. O The probability distribution of x is approximately normal with : 81 and 16.97. O The probability distribution of x is not normal. O The probability distribution of x is approximately normal with 81 and = 12.00. What is the probability that X

Explanation / Answer

Z =(X - 81)/24

P (X<40)=P (Z<1.71) = 0.0436

b)

option b) is correct

sd(Xbar) = 24/sqrt(n) = 24/sqrt(2) = 16.973

c)

P(Xbar < 40) =

P (Z<2.42)=0.0078

d)

for n = 3 , sd(Xbar) = 20/sqrt(3) = 11.5470053

P(Xbar< 40) =

P (Z<3.55)=0.0002

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