Which salesperson takes the call sets the sale

Question

Incoming sales calls are routed to one of two salespeople. Ann handles $25\%$ of the calls, and her sales average $200. Bob handles the other $75\%$ , and his sales average $120.

What sale amount should you expect from a randomly routed call?

Accepted Answer

Two stages: which salesperson the call is routed to, then the size of that person's sale. The tower rule blends their averages by call share: E[	ext{sale}] = E\big[\,E[	ext{sale} \mid 	ext{person}]\,\big]. Step 1, the conditional averages are given: Ann \200, Bob \120. Step 2, blend by each person's share of calls: E[	ext{sale}] = 0.25 	imes 200 + 0.75 	imes 120 = 50 + 90 = 140. You expect a sale of \140. Ann closes larger sales, but Bob takes three times as many calls, so the blend leans toward Bob's figure. Takeaway. Blend group means by their share of the whole. The result tilts towa…

Which salesperson takes the call sets the sale

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