Bobby Mae Hasbrook Huffelpuffer is one top sales people at "You Want It We Got It, Inc . " Ms . Hufflepufer intends to visit three prospects today .

Bobby Mae Hasbrook Huffelpuffer is one top sales people at “You Want It We Got It, Inc.” Ms. Hufflepufer intends to visit three prospects today. She will visit Prospects 1, 2 and 3 in order, but does not know what time of the day. Visiting during lunch-time can be problematic because she Ms. Huffelpuffer knows that many people leave the office to get their food. She would also prefer not to visit right after lunch because she knows some people may be sleepy and unable to pay close attention to what she has to say. Visiting at the end of the day can also be an issue because people are always in a rush to leave and she has to pick up her twins from daycare at 5:30 PM across town. Ms. Huffelpuffer estimates that the chance of making a sale on the visit with Prospect 1 is about 30%. The visit with Prospect 2 has about a 40% chance of resulting in a sale and she hopes the prospect is not eating lunch. The visit with Prospect 3 has about 50% more of a chance of making a sale than the chance with Prospect 1 because Ms. Hufflepuffer knows the receptionist very well. The visits are independent and the company’s new MBA just told Ms. Huffelpuffer that based on her records of prior prospect visits there is a correlation between the length of the visit and likelihood of a sale.

1. Construct a probability tree to produce the full probability distribution for the random variable “number of sales”.

2. Compute the expected number of sales and the standard deviation of the sales distribution.