For 5 year old children, the mean weight is 51.01 pounds with a standard deviation of 3.98 pounds.  Convert the following observations into z-scores. 45.67 50 63.44 48 56.81

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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For 5 year old children, the mean weight is 51.01 pounds with a standard deviation of 3.98 pounds.  Convert the following observations into z-scores.

45.67

50

63.44

48

56.81

Expert Solution
Step 1

The Z-score of a random variable X is defined as follows:

Z = (X  µ)σ.

Here, µ and σ are the mean and standard deviation of X, respectively.

In this context, X is raw score.

For X=45.67, the Z-score is,

Z = 45.67 51.013.98=-5.343.98=-1.34

For X=50, the Z-score is,

Z = 5051.013.98=-1.013.98=-0.25

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