The z score tells us how many standard deviations a value is from the mean of the distribution. When a z score is positive, the value is found to the right of the mean whereas a negative z score indicates the value is found to the left of the mean. For a value, x, from a dataset with mean and standard deviation, the following formula can determine the number of standard deviations x is from the mean and whether it is to the right or to the left. This formula can also be used to find the x value that is a given number of standard deviations from the mean. The distribution of calf maximum girths has a mean of 36.0694 centimeters, and standard deviation of 2.8492 centimeters. Use this information and the z score formula to determine the calf maximum girths that are one standard deviation to the left and right of the mean. -1 = To find the value that is one standard deviation to the left of the mean, set z = -1 and solve for x. (Round your final answer to two decimal places.) X-36.0694 ✓ x= -13.01 z = -2 = x To find the value that is one standard deviation to the right of the mean, set z = 1 and solve for x. (Round your final answer to two decimal places.) x- 36.0694 1 = 2.8492 X-H x = -12.30 x Find the calf maximum girths that are two standard deviations from the mean. To find the value that is two standard deviations to the left of the mean, set z = -2 and solve for x. (Round your final answer to two decimal places.) x-36.0694 2 = -3= 2.8492 x = -13.36 x To find the value that is two standard deviations to the right of the mean, set z = 2 and solve for x. (Round your final answer to two decimal places.) - 36.0694 2.8492 3 = x = -11.95 Find the calf maximum girths that are three standard deviations from the mean. To find the value that is three standard deviations to the left of the mean, set z = -3 and solve for x. (Round your final answer to two decimal places.) x - 36.0694 2.8492 x= -11.60 2.8492 x= -13.71 x To find the value that is three standard deviations to the right of the mean, set z = 3 and solve for x. (Round your final answer to two decimal places.) x- 36.0694 x 2.8492 x
The z score tells us how many standard deviations a value is from the mean of the distribution. When a z score is positive, the value is found to the right of the mean whereas a negative z score indicates the value is found to the left of the mean. For a value, x, from a dataset with mean and standard deviation, the following formula can determine the number of standard deviations x is from the mean and whether it is to the right or to the left. This formula can also be used to find the x value that is a given number of standard deviations from the mean. The distribution of calf maximum girths has a mean of 36.0694 centimeters, and standard deviation of 2.8492 centimeters. Use this information and the z score formula to determine the calf maximum girths that are one standard deviation to the left and right of the mean. -1 = To find the value that is one standard deviation to the left of the mean, set z = -1 and solve for x. (Round your final answer to two decimal places.) X-36.0694 ✓ x= -13.01 z = -2 = x To find the value that is one standard deviation to the right of the mean, set z = 1 and solve for x. (Round your final answer to two decimal places.) x- 36.0694 1 = 2.8492 X-H x = -12.30 x Find the calf maximum girths that are two standard deviations from the mean. To find the value that is two standard deviations to the left of the mean, set z = -2 and solve for x. (Round your final answer to two decimal places.) x-36.0694 2 = -3= 2.8492 x = -13.36 x To find the value that is two standard deviations to the right of the mean, set z = 2 and solve for x. (Round your final answer to two decimal places.) - 36.0694 2.8492 3 = x = -11.95 Find the calf maximum girths that are three standard deviations from the mean. To find the value that is three standard deviations to the left of the mean, set z = -3 and solve for x. (Round your final answer to two decimal places.) x - 36.0694 2.8492 x= -11.60 2.8492 x= -13.71 x To find the value that is three standard deviations to the right of the mean, set z = 3 and solve for x. (Round your final answer to two decimal places.) x- 36.0694 x 2.8492 x
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Understanding Z Scores and Calculating Values with Standard Deviations
**Z Score Definition**
The z score tells us how many standard deviations a value is from the mean of the distribution. When a z score is positive, the value is found to the right of the mean, whereas a negative z score indicates the value is found to the left of the mean.
For a value, \( x \), from a dataset with mean \( \mu \) and standard deviation \( \sigma \), the following formula can determine the number of standard deviations \( x \) is from the mean and whether it is to the right or to the left. This formula can also be used to find the \( x \) value that is a given number of standard deviations from the mean.
\[
z = \frac{x - \mu}{\sigma}
\]
---
**Problem Context**
The distribution of calf maximum girths has a mean of 36.0694 centimeters and standard deviation of 2.8492 centimeters. Use this information and the z score formula to determine the calf maximum girths that are one, two, and three standard deviations to the left and right of the mean.
---
**One Standard Deviation**
To find the value that is one standard deviation to the left of the mean, set \( z = -1 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
-1 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 - 2.8492 = 33.22
\]
To find the value that is one standard deviation to the right of the mean, set \( z = 1 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
1 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 + 2.8492 = 38.92
\]
---
**Two Standard Deviations**
To find the value that is two standard deviations to the left of the mean, set \( z = -2 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
-2 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 - 2(2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4971f23-5570-4fed-8cd6-5e1a07d18a42%2F381c661c-ddb0-4bed-b837-4399f1345c39%2Fno8xyu8_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Z Scores and Calculating Values with Standard Deviations
**Z Score Definition**
The z score tells us how many standard deviations a value is from the mean of the distribution. When a z score is positive, the value is found to the right of the mean, whereas a negative z score indicates the value is found to the left of the mean.
For a value, \( x \), from a dataset with mean \( \mu \) and standard deviation \( \sigma \), the following formula can determine the number of standard deviations \( x \) is from the mean and whether it is to the right or to the left. This formula can also be used to find the \( x \) value that is a given number of standard deviations from the mean.
\[
z = \frac{x - \mu}{\sigma}
\]
---
**Problem Context**
The distribution of calf maximum girths has a mean of 36.0694 centimeters and standard deviation of 2.8492 centimeters. Use this information and the z score formula to determine the calf maximum girths that are one, two, and three standard deviations to the left and right of the mean.
---
**One Standard Deviation**
To find the value that is one standard deviation to the left of the mean, set \( z = -1 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
-1 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 - 2.8492 = 33.22
\]
To find the value that is one standard deviation to the right of the mean, set \( z = 1 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
1 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 + 2.8492 = 38.92
\]
---
**Two Standard Deviations**
To find the value that is two standard deviations to the left of the mean, set \( z = -2 \) and solve for \( x \). (Round your final answer to two decimal places.)
\[
-2 = \frac{x - 36.0694}{2.8492}
\]
\[
x = 36.0694 - 2(2.
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