A salesman wants to know the average number of units he sells per sales call. He checks his past sales records and comes up with the following probabilities:: Sales (in units): 0 1 2 3 4 5 Probability 0.15 0.20 0.10 0.05 0.30 0.20 . What is the average number of units he sells per sale call?

Explanation

According to questiion:

The salesman wanted to know the average number of units he sells per sales call.This is the same as saying that he wanted to know the expected value of each sales call, where a sales call is the random variable x.

So, this can be calculated by the formula :

`{E}({x})={p}_{1} {x}_{1}+{p}_{2} {x}_{2}+{p}_{3} {x}_{3}+{p}_{4} {x}_{4}+{p}_{5} {x}_{5}+{p}_{5} {x}_{5} `

`=0.15 times 0+0.20 times 1+0.10 times 2+0.05 times 3+0.30 times 4+0.20 times 5 `

`=0+0.2+0.2+0.15+1.2+1.0=2.75`


Thus, he would expect to sell 2.75 or 3 units on each sales call.