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 u = 81 andestimated 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.O The probability distribution of x is not normal.O The probability distribution of x is approximately normal with uz = 81 and o, = 31.82.O The probability distribution of x is approximately normal with uz = 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 YesO NoExplain what this might imply if you were a doctor or a nurse.O The more tests a patient completes, the weaker is the evidence for lack of insulin.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.

Name: Let x be a random variable that represents the level of glucose in the
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 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

Given that, X~ Normal (mean= 81 , s.d.= 45) If sample size, n= 2 Then mean of X, X bar ~…

Answered: Let x be a random variable that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

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 ? = 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 u = 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.
O The probability distribution of x is not normal.
O The probability distribution of x is approximately normal with uz = 81 and o, = 31.82.
O The probability distribution of x is approximately normal with uz = 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.
O The more tests a patient completes, the weaker is the evidence for lack of insulin.
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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.