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TicketMaster and MasterTicket offer identical tickets to the same Broadway show

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TicketMaster and MasterTicket offer identical tickets to the same Broadway show. The number of tickets purchased at TicketMaster has a Normal distribution with mean 100 and standard deviation 10. The number of tickets purchased at MasterTicket is Normal with mean 200, and standard deviation 10. TicketMaster stocks up with 110 tickets, while MasterTicket stocks 220. A "stock-out" is the event in which

demand for tickets exceeds available stock.

 

a. What is the probability of "stock-out" at each tickets office?

 

The two tickets offices decide to merge and create new office MergeTic. The total number of tickets purchased at this new firm is the sum of the two previous ones.

 

b. Assuming the demand at the original ticket offices were independent, find the expected value and standard deviation of the number of tickets purchased at MergeTic?

 

c. MergeTic decides that their current stock level should simply be the combined stock levels that were used before, i.e., they maintain a stock of 330 tickets. What is the probability of "stock-out" with this policy assuming demands at the original ticket offices were independent?