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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 - 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

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 - 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

MATLAB: An Introduction with Applications
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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**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.
Transcribed Image Text:**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.
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