Continuous Probability Distributions- Statistics can someone solve the below problem?
Specialty faces the decision of how many Weather Teddy units to order fr the coming season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000 or 28,000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team ask you for an analysis of the stock out probabilities for various order quantities, an estimate of the profit potential and to help make an order quanity recommendation. Specialty expects to sell weather teddy for $24 based on a cost of $16 per unit, if inventory remains after the holiday season, Specialty will sell all surplus inventory for $5 per unit. After reviewing the sales history f similar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with .90 probability that demand would be between 10,000 units and 30,000 units.
1. use the sale forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation
2. compute the probability of a stock out for the order quantities suggested by members f the management team.
3. compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales=10,000 units , most likely case in which sales =20,000 units and best case in which sales = 30,000 units.
4. one of specialty's managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock outs. What quantity would be order under this policy and what is the projected profit under the three sales scenarios?
5. Provide your own reccommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation
a 95% probability changes the +/-1.645 to +/-1.960.
You get these by looking up the relevant probability P=1-(1-0.95)/2 in a table of the cumulative normal distribution (reverse look up in fact).
We are given mean=20000, then as 30000=20000+1.960*SD we find:
So you have a demand distribution N(20000,(10000/1.960)^2)