A heavy-equipment salesperson can contact either one or

Chapter 3, Problem 26E

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QUESTION:

Problem 26E

A heavy-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 .9 and .1, respectively. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.3

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QUESTION:

Problem 26E

A heavy-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 .9 and .1, respectively. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.3

ANSWER:

Solution 26E

Step1 of 3:

Let us consider a random variable “X” it presents daily sales and X can takes the values $0, $50,000, and $100,000 respectively. If X = 0, either the sales person contacted only one customer and failed to make a sale or the sales person contacted two customers and failed to make both sales. Salesperson can contact either one or two customers per day with probability 1/3 and 2/3, respectively, with the probabilities 0.9 and 0.1, respectively.

We need to find the mean and standard deviation of the daily sales.3.


Step2 of 3:

Take

= 0.3 + 0.54

                                                          = 0.84

Hence, P(X = 0) = 0.84.

If X = 2 the salesperson contacted two customers and made both sales.

So,

              = 0.00666

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