SeaFair Fashions relies on its sales force of 220 to do an i

SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashions. The company is presently bringing out a new line of swimwear and has invited 40 salespeople to its Orlando home office. An issue of 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 40 will have?

(B) Calculate the standard error of the sampling distribution of the sample means for all samples of size 40.

(C) What is the probability that the sample mean of 40 will have a sales average less than $400,000?

(D) How would the answers to parts a, b, and c change if the home office brought 60 salespeople to Orlando?

(E) Each year SeaFair invites the sales personnel with sales above the 85th percentile to enjoy a complimentary vacation to Hawaii. What is the smallest sales level for the sales personnel who were awarded a trip to Hawaii last year?

(F) SeaFair fashions divides its sales staff into 5 regions. Each region has 44 sales personnel. As an incentive they offer cash bonus to any region whose average in the current year is better than the third quartile for the previous year’s sales. What is the average sales a region would need to achieve for the members of the region’s sales staff to receive the cash bonus?

(F)

Solution