**Problem Statement:**Los Angeles workers have an average commute of 28 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let \( X \) represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.a. What is the distribution of \( X \)? \( X \sim N(\, \, \, \, , \, \, \,) \)b. Find the probability that a randomly selected LA worker has a commute that is longer than 33 minutes. \(\,\_\_\_\_\_\_\_\_\_\_\_\_\_\,\)c. Find the 90th percentile for the commute time of LA workers. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) minutes**Explanation:**- **Distribution of \( X \):** - The question asks to define the normal distribution for \( X \), given the mean and standard deviation, in the format \( X \sim N(\mu, \sigma^2) \).- **Probability Calculation:** - Calculate the probability that a commute time exceeds 33 minutes using the properties of the normal distribution.- **Percentile Calculation:** - Determine the 90th percentile of the commute times, which involves finding the value below which 90% of the observations fall in a normal distribution.

Given Data Population Mean,μ = 28 Population Standard Deviation,σ = 13

Answered: Los Angeles workers have an average…

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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