A large toy$-$store chain is considering the launch of a new toy, currently code$-$namedNoel$25,$ in time for Christmas $2025.$ The question the company faces is deciding howmany units to order from its manufacturers to meet anticipated sales demand. If too few are ordered, sales will be lost $($a stock$-$out$).$ If too many are ordered, losses will beincurred because of low prices realised in post$-$Christmas clearance sales.The companys sales analyst predicts an expected demand of $25,000$ units with a $0\mathrm{.}95$probability that demand will be between $15,000$ units and $35,000$ units. The four members of the management team have suggested order quantities for Noel$25$ of $20,000$; $24,000$; $27,000$; and $32,000$ units. The manufacturing and distribution cost is $20$ per unit. The company expects to sell Noel$25$ before Christmas for $30$ per unit. After the Christmas period, the company will sell surplus inventory for $10$ per unit.Prepare a report that addresses the following:a$.$ Using the sales analysts predictions, calculate the mean and standard deviation of anormal distribution that will approximate the probability distribution for demand. b$.$ Calculate the probability of a stock$-$out for the order quantity suggested by eachmember of the management team. c$.$ Calculate the projected profit for the order quantities suggested by the members of the management team under three scenarios: worst case, sales $=15,000$ units; mostlikely case, sales $=25,000$ units; best case, sales $=35,000$ units. d$.$ Suppose the payment to the manufacturer is made at the end of July $2025.$ Assumehalf the Christmas sales revenue is received at the end of November, half at the endof December, and the after$-$Christmas sales revenue is received at the end of January$2025.$ Assume $32,000$ units are ordered, and Christmas sales match the sales analysts expected demand figure. What is the projected profit at July $2024$ prices if adiscount rate of $0\mathrm{.}25\%$ per month is applied to the revenues?