**Understanding Z-Scores with Commuting Times**Consider the population of commuting time to school for all John Jay College students during Spring 2022. The commuting times have a mean of 95 minutes and a standard deviation of 22 minutes. One student from STA 250-99 class had a commuting time of 2 hours and 15 minutes. What is the z score for this commuting time? (Give your answer correct to two decimal places.)---### Analysis and Explanation:#### Definitions:1. **Mean (μ):** The average value of all the commuting times, which is 95 minutes.2. **Standard Deviation (σ):** A measure of how spread out the numbers are, which is 22 minutes.3. **Z-Score:** The number of standard deviations a data point is from the mean.#### Calculation Steps:1. **Convert the commuting time to minutes**: - 2 hours and 15 minutes = 2 * 60 + 15 = 120 + 15 = 135 minutes.2. **Apply the Z-Score formula**: \[ Z = \frac{(X - \mu)}{\sigma} \] Where: - $ X $ = observed value (135 minutes) - $ \mu $ = mean (95 minutes) - $ \sigma $ = standard deviation (22 minutes)3. **Substitute the values**: \[ Z = \frac{(135 - 95)}{22} \]4. **Calculate the Z-Score**: \[ Z = \frac{40}{22} \approx 1.82 \]#### Conclusion:The z score for the student's commuting time is approximately 1.82. This means the student's commuting time is 1.82 standard deviations above the mean commuting time.---**Note:** Z-Scores allow us to understand how a particular value compares to the overall distribution of the data. In this case, the student's commuting time is significantly above average.

Answered: Image /qna-images/answer/9080a7c3-e2e0-4226-bbc5-5026d347e7a0.jpg

Answered: Consider the population of commuting…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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