Question $3(30$ points$)$

For the coming season, Savannah Bee Company plans to introduce a new product called Orange Blossom Honey. Savannah Bee faces the decision of how many units of Orange Blossom Honey to produce for the coming holiday season. Members of the management team recommended production quantities of $1,500,1,800,2,400,$ and $2,800.$ The different production quantities reflect considerable disagreement regarding the market potential of the new product. The product management team has contracted you for an analysis of the stock out probabilities for various production quantities, an estimate of the profit potential, and to help make a production quantity recommendation. Savannah Bee expects to sell Orange Blossom Honey for $$20,$ and the cost is $$11$ per unit. If inventory remains after the holiday season, Savannah Bee will sell all surplus inventory for $$10$ per unit. After reviewing the sales history of similar products, Savannah Bee$$s senior sales forecaster predicted an expected demand of $2,000$ units with a $0\mathrm{.}9$ probability that demand would be between $1,000$ units and $3,000$ units.

a$\mathrm{.}6$ points: Please use sales forecaster$$s prediction to describe a normal probability distribution thatcan be used to approximate the demand distribution. Compute the normal distribution$$s standarddeviation. $($Place the answer in Cell C$2$ and the formula$($s$)$ in Cells G$2$:K$2)$