Question 3: Dum-Dum Sales actually buys the tickets from JHU that it resells by

Question

Question 3:
Dum-Dum Sales actually buys the tickets from JHU that it resells by phone. Fred and Ethel have to decide how many tickets to buy for the next game. They are having a discussion about how many to obtain. JHU is kind enough to sell tickets to Dum-Dum Sales at a cost of $10 each. Dum-Dum then resells the tickets for $12 each. The two owners are having an argument about how to make the decision. They already have 50 tickets in hand. They have two different ideas about buying one more ticket. Fred says “the probability of being able to sell one more ticket is the probability that demand is greater than 50. Therefore, we should get one more as long as $12 * PR(demand > 50) is more than $10.” Ethel counters by saying, “Fred, you are a real Dum- Dum. We may not be able to sell that additional ticket. I don’t think we should buy it unless {1 - Pr(demand < 51)} is more than 10/12.”

a. Which of the Dum-Dum twins is correct if demand follows a discrete distribution?
b. If demand were Normally distributed with a mean of 100 and a Standard Deviation of
20, how many tickets should they buy?
c. If they already have 50 tickets in hand how many more should they get?

Explanation / Answer

a.) Both of the Dum-Dum twins are correct...since both statements are equivalent.... b.) we should take Phi(x) = 10/12 ....where Phi(x) is Standard normal dist. density therefore x= -0.97 therefore they should buy = 100 - 0.97*20 = 80.6 = 81 tickets approx. c.) they should buy 31 more tickets...

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