### Understanding Z-Scores in a Normal DistributionIn this example, we will calculate the z-score of Rashid's height, given that the height of males in the United States is normally distributed with a specific mean and standard deviation.**Problem:**Rashid is 84 inches tall. If the height of males in the United States is normally distributed with:- a mean ($\mu$) of 70 inches- a standard deviation ($\sigma$) of 4 inchesWhat is the z-score of Rashid's height?**Solution:**To calculate the z-score of Rashid's height, we use the following formula:\[ z = \frac{(X - \mu)}{\sigma} \]Where:- $ z $ is the z-score- $ X $ is the value we are standardizing (Rashid's height, which is 84 inches)- $ \mu $ is the mean of the distribution (70 inches)- $ \sigma $ is the standard deviation of the distribution (4 inches)Plug in the values:\[ z = \frac{(84 - 70)}{4} \]\[ z = \frac{14}{4} \]\[ z = 3.5 \]**Interpretation:**A z-score of 3.5 indicates that Rashid's height is 3.5 standard deviations above the mean height of males in the United States. This means Rashid's height is significantly higher than the average male height in the United States.### Key Points:- The z-score allows us to understand how far a specific value is from the mean in terms of standard deviations.- A higher positive z-score indicates a value above the mean, while a negative z-score would indicate a value below the mean.- Understanding z-scores helps in comparing data points from different distributions or sets of data.Feel free to use this calculation method to determine z-scores for other sets of data that follow a normal distribution!

Height of Rashid = x = 84 inches. Mean = 70 Standard deviation = 4 The z-score is given by z-score…

Answered: Rashid is 84 inches tall. If the height…

Rashid is 84 inches tall. If the height of males in the United States is nor- mally distributed with a mean of 70 inches and a standard deviation of 4 inches, what is the z-score of Rashid's height?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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