Let x be a random variable that represents the level of glucosein the blood (milligrams per deciliter of blood) after a 12-hourfast. Assume that for people under 50 years old, x has adistribution that is approximately normal, with mean μ = 56 andestimated standard deviation σ = 25. A test result x < 40 is anindication of severe excess insulin, and medication is usuallyprescribed.
(a) What is the probability that, on a single test, x < 40?(Round your answer to four decimal places.)
- What is the probability that x < 40? (Round your answer tofour decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Roundyour answer to four decimal places.)
(d) Repeat part (b) for n = 5 tests taken a week apart. (Roundyour answer to four decimal places.)
(e) Compare your answers to parts (a), (b), (c), and (d). Didthe probabilities decrease as n increased?
