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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 u = 81 an estimated standard deviation o = 45. A test result x < 40 is an indication f severe excess insulin, and medication is usually prescribed. A USE SALT (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) 0.1811 (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. ao The probability distribution of x is not normal. bo The probability distribution of x is approximately normal with = 81 and o, = 31.82. Co The probability distribution of x is approximately normal with ug = 81 and oz = 22.50. 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.) 0.0572 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 0.0211 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No Explain what this might imply if you were a doctor or a nurse. a O The more tests a patient completes, the weaker is the evidence for lack of insulin. b O The more tests a patient completes, the stronger is the evidence for lack of insulin. O The more tests a patient completes, the stronger is the evidence for excess insulin.

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 = 81 an estimated standard deviation o = 45. A test result x < 40 is an indication f severe excess insulin, and medication is usually prescribed. A USE SALT (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) 0.1811 (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. ao The probability distribution of x is not normal. bo The probability distribution of x is approximately normal with = 81 and o, = 31.82. Co The probability distribution of x is approximately normal with ug = 81 and oz = 22.50. 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.) 0.0572 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 0.0211 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No Explain what this might imply if you were a doctor or a nurse. a O The more tests a patient completes, the weaker is the evidence for lack of insulin. b O The more tests a patient completes, the stronger is the evidence for lack of insulin. O The more tests a patient completes, the stronger is the evidence for excess insulin.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 58CR
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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 ? = 81 and estimated standard deviation ? = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(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.

What is the probability that x < 40? (Round your answer to four decimal places.)

Explain what this might imply if you were a doctor or a nurse. (Select one of the options in screenshot)

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 p = 81 and estimated standard deviation o = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. n USE SALT (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) 0.1811 (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. a o The probability distribution of x is not normal. bo The probability distribution of x is approximately normal with µz = 81 and o, = 31.82. C O The probability distribution of x is approximately normal with µz = 81 and o, = 22.50. 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.) 0.0572 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 0.0211 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No Explain what this might imply if you were a doctor or a nurse. a O The more tests a patient completes, the weaker is the evidence for lack of insulin. bo The more tests a patient completes, the stronger is the evidence for lack of insulin. O The more tests a patient completes, the stronger is the evidence for excess insulin.
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 p = 81 and estimated standard deviation o = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. n USE SALT (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) 0.1811 (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. a o The probability distribution of x is not normal. bo The probability distribution of x is approximately normal with µz = 81 and o, = 31.82. C O The probability distribution of x is approximately normal with µz = 81 and o, = 22.50. 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.) 0.0572 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 0.0211 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No Explain what this might imply if you were a doctor or a nurse. a O The more tests a patient completes, the weaker is the evidence for lack of insulin. bo The more tests a patient completes, the stronger is the evidence for lack of insulin. O The more tests a patient completes, the stronger is the evidence for excess insulin.
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