The business school at State university currently has three

The business school at State university currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, and average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking stickers show up.

Questions:

A) given the current situation, estimate the probability that on a peak day, at least 1 faculty member with a sticker will be able to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other 2 lots. Compare the 2 situations: 1) each person can park only in the lot assigned to him/her, and 2) each person can parkk in any of the lots (pooling). (hint: use RISKBINOMIAL function)

B) Now suppose the number of people who show up at the 3 lots are highly correlated (corr .9). How are the results different frmo those in part a?

Solution

A) 1) P [ Atleast one faculty member with a sticker will be able to find a spot in his particular lot ]
= 1 - P [ No faculty member with a sticker will be able to find a spot in his particular lot ]
=1 - [ (45/200)* ( 0.7 + 0.72+0.74) ] = 0.514..


2) = 1 - P [ no faculty member with a sticker will be able to find a spot in any of the lots ]
= 1 - [ (45/200) * 0.72 ] = 0.838..

b) Values won\'t change because independence is not reqd. here at all!