Solve the questions in detail and provide the explanations

5.) In the past Mr X's retail store has a very good service record. Most of the products were in stock whenever a customer visited. In order to maintain high service rate , how many packs of FruityNut Juice should Mr X order for maintaining 95% in-stock probability?

Hint: F(-1.25)= 0.1056, F(2.5) = 0.9938, F(-0.5)=0.3085 , F(0.5)=0.6915, F(1.65)=0.95

Q1) Mr. X owns a retail story in Old Delhi. A juice manufacturing company Fruitify is planning to expand market by launching its juice category named FruityNut in various places of Delhi. Company Fruitify contacts Mr. X and request his to stock its new juice category FruityNut in the retail store shelf. The retail price for each pack of FruityNut is Rs. 20 and the wholesale price is Rs. 12. The company Fruitify offers a contract to share the risk of Mr. X. The contract terms and conditions states that the Fruitify will buy back the unsold inventory at a full refund. However, it cost approximately Rs. 4 to the Mr. X for returning each pack of unsold juice. The demand forecast data for the similar category juice (from other markets) shows that the weekly demand follows a a normal distribution with mean 200 and standard deviation 80 . Now, Mr X should decide the order quantity of FruityNut juice and place the order to the company. i. Mr X will consider the FruityNut juice to be a success or winning deal if he is able to sell more than 400 packs weekly. What is the probability that FruityNut juice is a success in the market? ii. MrX will consider FruityNut juice a failure product in the market if sells less than 50 percent of his mean forecast. What is the probability FruityNut juice is a failure? iii. What is the probability demand for FruityNut juice will be within 20 percent of the mean forecast? iv. What will be the expected profit maxipizing order quantity for FruityNut juice