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

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

Hence, P(X = 2) = 0.00666.

Similarly,

P(X = 1) = 1 - 0.84 - 0.00666

= 0.15334

Hence, P(X = 1) = 0.15334.

Step3 of 3:

Consider,

Mean of the daily sales 3 is given by:

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