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 u = 74 and estimated standard deviation o = 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.) 0.1038 (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. O The probability distribution of x is approximately normal with u, = 74 and o, = 13.50. O The probability distribution of x is approximately normal with u, = 74 and o, = 27. O The probability distribution of x is approximately normal with u, = 74 and o, = 19.09. O The probability distribution of x is not normal. What is the probability that x < 40? (Round your answer to four decimal places.) 19.09 (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) 15.5885 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 12.0748
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 u = 74 and estimated standard deviation o = 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.) 0.1038 (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. O The probability distribution of x is approximately normal with u, = 74 and o, = 13.50. O The probability distribution of x is approximately normal with u, = 74 and o, = 27. O The probability distribution of x is approximately normal with u, = 74 and o, = 19.09. O The probability distribution of x is not normal. What is the probability that x < 40? (Round your answer to four decimal places.) 19.09 (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) 15.5885 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 12.0748
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text: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 u = 74 and estimated standard deviation o = 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.)
0.1038
(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.
O The probability distribution of x is approximately normal with u, = 74 and o, = 13.50.
O The probability distribution of x is approximately normal with u, = 74 and o, = 27.
O The probability distribution of x is approximately normal with u, = 74 and o, = 19.09.
O The probability distribution of x is not normal.
What is the probability that x < 40? (Round your answer to four decimal places.)
| 19.09
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
15.5885
(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
12.0748
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