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
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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