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 ~ N(,)
b. Find the probability that a randomly selected LA worker has a
commute that is longer than 32 minutes.
c. Find the 75th percentile for the commute time of LA
workers. minutes
Solution:
Let X be the commute time for randomly selected LA workers.
With mean = 33 minutes and standard deviations = 13 minutes.
a) The distribution of X is
b) To find P( X > 32 )
= P( Z > - 0.076923)
= P( Z > -0.08)
= P( Z < 0.08)
= 0.5319 from Z t
P( X > 32) = 0.5319
c) To find 75th percentile.
P( X < k ) = 0.75
c = 0.67 from Z table .
K = 33 + 13 *0.67
K = 33+ 8.71
K = 41.71
K= 42
The 75th percentile of commute time of LA workers is 42
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