Question

A study was conducted to find information on the heights of race jockeys. The data was found to be normally distributed with a mean of 60 in and a standard deviation of 2.3 in. What is a jockey's z-score if they have a height of 58 in?

Answer 1

The z-score of a jockey with a height of 58 inches is -0.8696, indicating they are shorter than the average race jockey.

Step-by-step explanation:

To calculate the z-score of a jockey with a height of 58 inches, we use the z-score formula:

z = (X - μ) / σ

Where:

• X is the value in the dataset (the jockey's height)
• μ (mu) is the mean of the dataset (average height)
• σ (sigma) is the standard deviation of the dataset

Given that the mean height μ is 60 inches and the standard deviation σ is 2.3 inches, we substitute:

z = (58 - 60) / 2.3

This equals:

z = -2 / 2.3

z = -0.8696

A z-score of -0.8696 means the jockey's height is 0.8696 standard deviations below the mean. This indicates that the jockey is shorter than the average race jockey.