The professor has ranted during the semester about his parking woes. Although he
ID: 3227869 • Letter: T
Question
The professor has ranted during the semester about his parking woes. Although he knows there is a parking place available somewhere on campus when he arrives, he does not always find it easily. Once he found a spot within five minutes of arriving on campus. The longest if has ever taken him was a terrible day that needed 45 minutes. He had to jog to class and the students laughed at his huffing and puffing. (Maybe spend a little more time on the treadmill, huh?) He kept track for the first half of the semester and found the mean time to find a spot was 25 minutes and the times were normally distributed.
He would be happy if he could be on time 90% of the time. Class starts at 12:30. It takes 10 minutes to walk from any parking spot on campus to class.
From a statistical point of view, why is this a problem. Using the things we have discussed in class, what is your best suggestion for him?
Looking for help in the right direction, so far I think there isn't an answer or if there is it's to use the range rule of thumb which just ends in an estimation and isn't as precise. Is there a precise way to get what he's looking for?
Explanation / Answer
Statistical solution to Professor’s problem would be to find the 90 perccntile of the time taken to find a parking spot, then back-track the time to decide the latest time by which the Professor should reach the campus.
Let X = Time taken to find a parking spot. Then, we are given X ~ N(25, ), being unknown.
Interpreting, ‘Once he found a spot within five minutes of arriving on campus. The longest it has ever taken him was a terrible day that needed 45 minutes.’ To mean that the total spread of X is 40 minutes and equating it to 6, we estimate as 7.
We want P(X < t) = 0.90 (i.e., 90%) => P[Z < {(t - 25)/7}] = 0.9 => {(t - 25)/7} = 1.284 [using Excel Function] => t = 33.99 ~ 34 minutes.
Back-tracking, the Professor should reach the campus 12:30 – (10 + 34) = 11: 46 ANSWER
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.