Question

Los Angeles workers have an average commute of 33 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 4 decimal places where possible. a. What is the distribution of X? X-NG b. Find the probability that a randomly selected LA worker has a commute that is longer than 39 minutes. c. Find the 90th percentile for the commute time of LA workers. minutes Question Help: Read Video Video Message instructor

Answer 1

Solution :

Given that ,

a) The distribut is normal X $\sim$ N (33 , 13)

b) P(x > 39 ) = 1 - p( x< 39)

=1- p P[(x - $\mu$) / $\sigma$ < (39 - 33) / 13]

=1- P(z < 0.46)

= 1 - 0.6772

= 0.3228

c) Using standard normal table,

P(Z < z) = 90%

= P(Z < 1.28) = 0.90  

z = 1.28

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.28 * 13 + 33

x = 49.64