Question

# Los Angeles workers have an average commute of 30 minutes. Suppose the LA commute time is...

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

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.

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