Question

Los Angeles workers have an average commute of 30 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 12 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 35 minutes.

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

Answer 1

a) We are given the distribution here as:

b) The probability here is computed as:

P(X > 35)

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.3385 is the required probability here.

c) From standard normal tables, we have:

P(Z < 1.2815) = 0.9

Therefore the required value here is computed as:

= Mean + 1.2815*Std Dev = 30 + 1.2815*12 = 45.378

Therefore 45.378 minutes is the required value here.