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StatisticsQ&A LibraryLos Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 14 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 30 minutes. c. Find the 85th percentile for the commute time of LA workers. minutesQuestion

Asked Feb 29, 2020

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Los Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 14 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 30 minutes.

c. Find the 85th percentile for the commute time of LA workers. minutes

Step 1

Let *X* be the commute time.

It is given that *X* is normally distributed with mean 27 minutes and standard deviation is 14 minutes.

**a).**

The distribution of *X* is given as** X~N(µ=27, σ^{2}=14).**

Step 2

**b).**

The probability that a randomly selected LA worker has a commute that greater than 30 minutes is calculated as follows:

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