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

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Statistics

Let x be a random variable that represents the level ofglucose in the blood (milligrams per deciliter of blood) after a 12hour fast. Assume that for people under 50 years old, xhas a distribution that is approximately normal, with meanμ = 69 and estimated standard deviation σ = 44. Atest result x < 40 is an indication of severe excessinsulin, 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 abouta week apart. What can we say about the probability distribution ofx? Hint: See Theorem 6.1.

The probability distribution of x is approximately normal withμx = 69 and σx = 44.

The probability distribution of x is not normal.  

   The probability distribution of x isapproximately normal with μx = 69 and σx =31.11.

The probability distribution of x is approximately normal withμx = 69 and σx = 22.00.


What is the probability that x < 40? (Round your answer to fourdecimal 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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