Question

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean $\mu = 87$ and standard deviation $\sigma = 26$. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) USE SALT (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125)

          A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is approximately normal with mean $\mu = 87$ and standard deviation $\sigma = 26$. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
USE SALT
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 125 (borderline diabetes starts at 125)

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A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour
fast, the random variable x will have a distribution that is approximately normal with mean μ = 87 and standard deviation σ = 26. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
USE SALT
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 125 (borderline diabetes starts at 125)

Added by Angela H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jen H

06/12/2023

Step 1

For (a) x > 60: z = (60 - 90) / 15 = -2 For (b) x < 110: z = (110 - 90) / 15 = 1.33 For (c) 60 < x < 110: z1 = (60 - 90) / 15 = -2 z2 = (110 - 90) / 15 = 1.33 For (d) x > 125: z = (125 - 90) / 15 = 2.33 Show more…

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Deviation tends to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125) A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x has a normal distribution with mean μ = 90 and standard deviation σ = 15.

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00:01 Here we want to find the probability that for an adult after 12 hours of fasting, x is going to be more than 60, less than 110, between 60 and 110, and then greater than 125.

00:30 We have that this is approximately normal with a mean of 80 and a standard deviation of 27.

00:46 And because we know the population standard deviation, we can do a z -score.

00:50 So i'm going to do z equals 60 minus 80 over 27, z equals 110, oops, minus 80 over 27, and z equals 125 minus 80 over 27.

01:22 And i'm going to calculate these z -scores.

01:24 So we're just going to type this in the calculator.

01:27 60 minus 80 divided by 27 is negative 0 .74.

01:32 110 minus 80 is 30 divided by 27 is 1 .11.

01:42 Then 125 minus 80 divided by 27 is 1 .67.

01:52 We're going to find the probabilities now.

01:56 So i'm going to need to put in a z -chart real quick.

01:58 So i'm going to bring this down.

02:08 I'm also going to make it smaller so that we can see both sides of the chart.

02:13 So let's go back up to part a.

02:18 I want to find the probability that x is greater than 60.

02:21 That's equivalent to finding the probability that z is greater than negative 0 .74.

02:28 So i'm going to go down to the chart and look for negative 0 .74.

02:35 So negative 0 .701234 .2296.

02:45 And charts give you probability of less than.

02:48 So if you need greater than, you have to do 1 minus that...

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