Question

Reports claim that the average daily driving time for commuters in the US is 120 minutes (µ=120). Assume that daily driving time is normally distributed with a standard deviation of 30 minutes (σ=30). Suppose that Mr. Smith’s driving time is in the top 3% of the US.

h)     Mr. Lopez just moved to a new city for a job. He now drives 10 minutes each way for work (20mins total). Is his driving an outlier?

i)     What is the probability of a randomly selected commuter having a commute of 125 minutes?

Answer 1

h) Z Score for mr. Lopez = (20-120)/30 = -100/30 = -3.33

Above Z score means that time taken by Mr. Lopez is 3.33 deviation less than or to the left of mean by 3.33 std. deviation. By definition of considering any point outside of +/-3 std. deviation, Mr. Lopez time to drive is an outlier.

i) Z score for 125 minutes = (125-120)/30 = 5/30 = .167

Area to the right of 0.167 std deviation to the right of mean = 0.44

Area to the left = 0.56

It means there is .44 probability that time taken is more than 125 minutes while .56 probability that time taken is less than or equal to 125 minutes.