At U of A, newly enrolled freshmen students are notorious for wanting to drive their cars to class (even though most of them are required to live on campus and can conveniently make use of the university’s free transit system). During the first couple of weeks of the fall semester, traffic havoc prevails on campus as first-year students try desperately to find parking spaces. With unusual dedication, the students wait patiently in the lanes of the parking lot for someone to leave so they can park their cars. Let us consider a specific scenario: The parking lot has 30 parking spaces but can also accommodate 10 more cars in the lanes. These additional 10 cars cannot park in the lanes permanently and must await the availability of one of the 30 parking spaces.

Freshman students arrive at the parking lot according to a Poisson distribution, with a mean of 20 cars per hour. The parking time per car averages about 60 minutes but actually follows an exponential distribution.

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(a) What is the percentage of freshmen who are turned away because they cannot enter the lot?

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(b) What is the probability that an arriving car will wait in the lanes?

(c) What is the probability that an arriving car will occupy the only remaining parking space on the lot?

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(d) Determine the average number of occupied parking spaces.

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(e) Determine the average number of spaces that are occupied in the lanes.

(f) Determine the number of freshmen who will not make it to class during an 8-hr period because the parking lot is totally full.