Homework Help is Here – Start Your Trial Now!
Math
Statistics
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?

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
Section13.3: Special Probability Density Functions
Problem 8E
See similar textbooks
icon
Related questions
Question
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
SEE MORE TEXTBOOKS