Los Angeles workers have an average commute of 29 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 two decimal places.

A. X ~ N( , )

B. Find the probability that a randomly selected LA worker has a commute that is longer than 40 minutes.

C. Find the 90th percentile for the commute time of LA workers.

a)

b) 0.1987

c)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  29 minutes

Standard Deviation, σ = 13 minutes

We are given that the distribution of commute time is a bell shaped distribution that is a normal distribution.

a) Distribution of X

Let X represent the commute time for a randomly selected LA worker. Then,

b) Probability that a randomly selected LA worker has a commute that is longer than 40 minutes

Calculation the value from standard normal z table, we have,  

c) 70th percentile for the commute time of LA workers.

We have to find the value of x such that the probability is 0.7

Calculation the value from standard normal z table, we have,  

The 70th percentile for the distribution of commute time of LA workers is 35.81 minutes.

add an !

step-by-step explanation:

5/12, or 5: 12

step-by-step explanation: