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Q 15

Expert-verified

Found in: Page 385

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

15. Suppose X ~ N(2, 6). What value of x has a z-score of three?

The value of $x$ is $20$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 Given Information

Given that,

$z = 3$ And,

$X ~ N (2, 6)$ Where,

$μ = 2$

$σ = 6$

Step 2 Explanation

We can Calculate the value of the $z -$ score as below:

$z = \frac{x - μ}{σ}$

Substitute the provided values in the above expression. Then,

$3 = \frac{x - 2}{6}$

$x - 2 = 3 \times 6$

$x = 18 + 2$

$x = 20$

Most popular questions for Math Textbooks

In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for President Clinton.

The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district.

a. State the approximate distribution of X.

b. Is 1,956.8 a population mean or a sample mean? How do you know?

c. Find the probability that a randomly selected district had fewer than 1,600 votes for President Clinton. Sketch the graph and write the probability statement.

d. Find the probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton.

e. Find the third quartile for votes for President Clinton.

Use the following information to answer the next four exercises:

$X ~ N (54, 8)$

Find the probability that $x > 56 .$

Kyle’s doctor told him that the z-score for his systolic blood pressure is $1.75$ . Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean $µ = 125$ and standard deviation $σ = 14$ . If X = a systolic blood pressure score then $X ~ N (125, 14)$ .

a. Which answer(s) is/are correct?

Kyle’s systolic blood pressure is $175$ .
Kyle’s systolic blood pressure is $1.75$ times the average blood pressure of men his age.
Kyle’s systolic blood pressure is $1.75$ above the average systolic blood pressure of men his age. i
Kyles’s systolic blood pressure is $1.75$ standard deviations above the average systolic blood pressure for men.

b. Calculate Kyle’s blood pressure.

How would you represent the area to the left of one in a probability statement?

An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of $280$ days and a standard deviation of $13$ days. An alleged father was out of the country from $240$ to $306$ days before the birth of the child, so the pregnancy would have been less than $240$ days or more than $306$ days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the localid="1653472319552" $z$ -scores first, and then use those to calculate the probability.

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Introductory Statistics

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Short Answer

15. Suppose X ~ N(2, 6). What value of x has a z-score of three?

Step by Step Solution

Step 1 Given Information

Step 2 Explanation

Most popular questions for Math Textbooks

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Introductory Statistics

Answers without the blur.

Short Answer

15. Suppose X ~ N(2, 6). What value of x has a z-score of three?

Step by Step Solution

Step 1 Given Information

Step 2 Explanation

Most popular questions for Math Textbooks

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