1 You are a vendor selling programs in front of the stadium of a certain pro football team that has not had a playoff win in over 10000days. You have the chance to buy programs from the printer for $0.30 a copy, that you will in turn resell for $10. The demanddistribution is expected to be normal with a mean = 265 and standard deviation = 53. After the game, any leftover copies will beworthless (nobody will want to remember the game).a. How many programs should you buy? Round your z value to 2 decimal places (e.g., 0.58) and your final answer to the nearest wholenumber.Optimal order quantiltyb. Based on the optimal quantity (before rounding), what is the approximate probability that you will run out of stock? Hint: Think aboutthe service level that you found for part a to identify the optimal quantity (before rounding), and then thínk about the relationshipbetween that service level and the probability of running out of stock (don't overthink this by adjusting for the fact that you roundedyour answer for part a). Round your answer to the nearest whole percent (e.g. if the answer is 83.6%, enter 84, not 84 or 84%).Probability

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You are a vendor selling programs in front of the stadium of a certain pro football team that has not had a playoff win in over 10000 days. You have the chance to buy programs from the printer for $0.30 a copy, that you will in turn resell for $110. The demand distribution is expected to be normal with a mean = 265 and standard deviation = 53. After the game, any leftover copies will be worthless (nobody will want to remember the game). a. How many programs should you buy? Round your z value to 2 decimal places (e.g., 0.58) and your final answer to the nearest whole number. Optimal order quantily b. Based on the optimal quantity (before rounding), what is the approximate probability that you will run out of stock? Hint: Think about the service level that you found for part a to identify the optimal quantity (before rounding), and then think about the relationship between that service level and the probability of running out of stock (don't overthink this by adjusting for the fact that you rounded your answer for part a). Round your answer to the nearest whole percent (e.g. if the answer is 83.6%, enter 84, not 84 or 84%). Probability