An automobile dealership recorded the number of cars sold daily over a certain p

Question

An automobile dealership recorded the number of cars sold daily over a certain period of time. These data was used in calculating the Probability Distribution of daily sales (X) provided below. Answer the following questions. How many cars, on average, does this dealership expects to sell daily 2 4 None of the above Find the Expected Value of X^3 5.6 17 None of the above What is the Probability of selling at most 3 cars daily? 0.9 0.3 None of the above Find the Standard Deviation of daily sales. 1.6 1.26 None of the above

Explanation / Answer

1) 0.2 + 0.1 + 0.3 + P(3) + 0.1 = 1

or, P(3) = 0.3

Average , E(X) = 0 * 0.2 + 1 * 0.1 + 2 * 0.3 + 3 * 0.3 + 4 * 0.1 = 2

Option-A) 2

2) E(X3) = 03 * 0.2 + 13 * 0.1 + 23 * 0.3 + 33 * 0.3 + 43 * 0.1

              = 17

Option-B) 17

3) P(X < 3) = 1 - P(X = 4)

                  = 1 - 0.1

                  = 0.9

Option-A) 0.9

4) E(X2) = 02 * 0.2 + 12 * 0.1 + 22 * 0.3 + 32 * 0.3 + 42 * 0.1

             = 5.6

Var(X) = E(X2) - (E(X))2

           = 5.6 - (2)2

           = 1.6

Standard deviation = sqrt(1.6) = 1.26

Option-B) 1.26

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