The business school at State university currently has three parking lots, each c

Question

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?

Explanation / Answer

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!

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