Aheavy-equipment salesperson can contact either one or two customers per day with probability 1/3 and 2/3, respectively. each contact will result in either no sale or a $50,000 sale, with the probabilities 0.9 and 0.1, respectively. find the mean and standard deviation of the daily sales. (hint: first obtain the probability distribution for daily sales.)

The mean of daily sales is $8,333.33 and the standard deviation of daily sales $19,507.83.

We arrive at the answer as follows:

1. Obtaining probability distribution for daily sales

On any day, the number of sales may be either 0 ,1 or 2.

We compute each of the probabilities as:

Since we know the P(X=0) and P(X=1), we can calculate P(X=2) as:

Now that we have the Probability distribution of daily sales, we can compute the mean of daily sales as follows:

Let V be value of sales per day, the mean is

Daily Sales       P          Value of sales -v                       v*P

     0           0.8400                     0                                        0

    1             0.1533               50000                           7666.666667

    2              0.0067              100000                              666.666667

Total               1                                                             8333.333333

The total in the table above is the mean of daily sales.

We calculate Standard Deviation as

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