Just please change the mark down from $29 to $26. Use normal probability distribution.

11. 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