Question

Los Angeles workers have an average commute of 31 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 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 37 minutes.

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

Answer 1

a)
X ~ N(31, 15)

b)
Here, μ = 31, σ = 15 and x = 37. We need to compute P(X >= 37). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (37 - 31)/15 = 0.4

Therefore,
P(X >= 37) = P(z <= (37 - 31)/15)
= P(z >= 0.4)
= 1 - 0.6554
= 0.3446

c)
z-value = 1.04

x = 31 + 1.04*15
x = 46.6 mins