# Let x be a random variable tha

**Question description**

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 = 52 and estimated standard deviation σ = 27. 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 μx = 52 and σx = 13.50.The probability distribution of x is approximately normal with μx = 52 and σx = 27. The probability distribution of x is not normal.The probability distribution of x is approximately normal with μx = 52 and σx = 19.09.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? YesNo Explain what this might imply if you were a doctor or a nurse.The more tests a patient completes, the stronger is the evidence for lack of insulin.The more tests a patient completes, the weaker is the evidence for lack of insulin. The more tests a patient completes, the weaker is the evidence for excess insulin.The more tests a patient completes, the stronger is the evidence for excess insulin.

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