SeaFair Fashions relies on its sales force of 400 to do an initial screening of all new fashions. The company is presently bringing out a new line of swimwear and has invited 30 salespeople to its Orlando home office. An issue of constant concern to the SeaFair sales office is the volume of orders generated by each salesperson. Last year the overall company average was $417,330 with a standard deviation of $45,285.
a. What shape do you think the distribution of all possible sample means of 30 will have? Discuss.
b. Determine the value of the standard deviation of the distribution of the sample mean of all possible samples of size 30.
c. Determine the probability that the sample of 30 will have a sales average less than $400,000.
d. How would the answer to part a, b, and c change if the home office brought 60 salespeople to Orlando? Provide the respective answers for this sample size.
e. Each year SeaFair invites the sales personnel with sales above the 80th percentile to enjoy a complimentary vacation in Hawaii. Determine the smallest sales level for the sales personnel who were awarded a trip to Hawaii last year. (Assume the distribution of sales was normally distributed last year).