SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashions. The company is currently bringing out a new line of swimwear and has invited 40 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. (Hint: The finite population correction factor, Equation 7.5, is required.)
a. Determine the probability the sample of 40 will have a sales average less than $400,000.
b. What shape do you think the distribution of all possible sample means of 40 will have? Discuss.
c. Determine the value of the standard deviation of the distribution of the sample mean of all possible samples of size 40.
d. How would the answers to parts 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 85th percentile to enjoy a complementary vacation in Hawaii. Determine the smallest average salary for the sales personnel that were in Hawaii last year. (Assume the distribution of sales was normally distributed last year.)