# Find Percentiles from a Given Normal Distribution

Your firm is attempting to reduce its cost of maintenance of customers by culling the least-productive of them. A census of sales records was undertaken and it was determined that the mean level of sale of all customers was $235,000 with a standard deviation of $15,000.

(a) It is your desire to eliminate from your customer portfolio those who are in the bottom ten percent of all customers. What would be the cut-off value (the least sales level) that would argue for keeping a specific customer?

(b) You are also considering creating a "star" class of customers that would receive special treatment. These customers would have to be in the top five percent of all customers. What level of purchases (sales to them) would they have to maintain to be considered "stars"?

(c) Discuss the nature of data used in (a) and (b). Why are we using the terms "mu" and "sigma" in this analysis? What are the implications of the use of these variables?

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#### Solution Summary

The solution finds percentiles from a given normal distribution. All calculations are shown along with detailed explanations.