Question: Irwin's sells a particular model of fan, with most of the sales being made in the summer months. Irwin's makes a one-time purchase of the fans prior to each summer season at a cost of $40 each and sells each fan for $60. Any fans unsold at the end of the summer season are marked down to $29 and sold in a special fall sale. Virtually all marked-down fans are sold. The following is the number of sales of fans during the past 10 summers: 30, 50, 30, 60, 10, 40, 30, 30, 20, 40.
a. Estimate the mean and the variance of the demand for fans each summer.
b. Assume that the demand for fans each summer follows a normal distribution, with mean and variance given by what you obtained in part (a). Determine the optimal number of fans for Irwin's to buy prior to each summer season.
c. Based on the observed 10 values of the prior demand, construct an empirical probability distribution of summer demand and determine the optimal number of fans for Irwin's to buy based on the empirical distribution.
d. Based on your results for parts (b) and (c), would you say that the normal distribution provides an adequate approximation?