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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 = 78 and estimated standard deviation = 44. 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 μ = 78 and ox= 31.11. The probability distribution of x is not normal. ● The probability distribution of x is approximately normal with μ The probability distribution of x is approximately normal with μ = 78 and What is the probability that X < 40? (Round your answer to four decimal places.) = 78 and 6 (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) Yes = 22.00. = 44. (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 5 No (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

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 = 78 and estimated standard deviation = 44. 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 μ = 78 and ox= 31.11. The probability distribution of x is not normal. ● The probability distribution of x is approximately normal with μ The probability distribution of x is approximately normal with μ = 78 and What is the probability that X < 40? (Round your answer to four decimal places.) = 78 and 6 (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) Yes = 22.00. = 44. (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 5 No (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 = 78 and estimated standard deviation o = 44. 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.) 1 (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 The probability distribution of x is not normal. The probability distribution of x is approximately normal with Mx The probability distribution of x is approximately normal with Mx = 78 and ox = 31.11. = 78 and ox = 78 and ox What is the probability that x < 40? (Round your answer to four decimal places.) 3 22.00. = 44. (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) 4 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 5 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? Yes No
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 μ = 78 and estimated standard deviation o = 44. 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.) 1 (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 The probability distribution of x is not normal. The probability distribution of x is approximately normal with Mx The probability distribution of x is approximately normal with Mx = 78 and ox = 31.11. = 78 and ox = 78 and ox What is the probability that x < 40? (Round your answer to four decimal places.) 3 22.00. = 44. (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) 4 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 5 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? Yes No
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