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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

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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 = 23. 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 not normal.

The probability distribution of x is approximately normal with μ_x = 54 and σ_x = 23.    

The probability distribution of x is approximately normal with μ_x = 54 and σ_x = 16.26.

The probability distribution of x is approximately normal with μ_x = 54 and σ_x = 11.50.

 

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.)