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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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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 μ and standard deviation o, 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.
-1 =
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.
Z =
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
x = -12.30
x-μ
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 =
X = -13.36
0
X = -11.95
2.8492
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 =
X = -13.71
X = -11.60
2.8492
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.)
x - 36.0694
2 =
2.8492
2.8492
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
-3 =
X
2.8492
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
3 =
2.8492
X
Transcribed Image Text: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 μ and standard deviation o, 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. -1 = 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. Z = 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 x = -12.30 x-μ 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 = X = -13.36 0 X = -11.95 2.8492 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 = X = -13.71 X = -11.60 2.8492 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.) x - 36.0694 2 = 2.8492 2.8492 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 -3 = X 2.8492 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 3 = 2.8492 X
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