An employee for a vending concession at a baseball stadium much choose between w

Question

An employee for a vending concession at a baseball stadium much choose between working behind the hot dog counter and receiving a fixed sum of $50 for the evening, or walking around the stands selling beer on a commission basis. If he sells beer, the employee can make $90 on a warm night, $70 on a moderate night, $45 on a cool night, and $15 on a coold night. At this time of the year the probabilities of a warm, moderate, cool, or cold night are .1, .3, .4, and .2, respectively.

a. Determine the mean or expected value to be earned (per night) by selling beer.

b. Computer the standard deviation of nightly earnings selling beer.

c. Which product should the employee sell (hot dogs or beer)? Why?

Explanation / Answer

a) Mean, E(X) = 90 * 0.1 + 70 * 0.3 + 45 * 0.4 + 15 * 0.2

                       = $51

b) E(X2) = 902 * 0.1 + 702 * 0.3 + 452 * 0.4 + 152 * 0.2

              = 3135

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

           = 3135 - 512

           = 534

Standard deviation = sqrt(534) = 23.1

c) The employee should sell beer. Because expected value to be earned by selling beer is $51 which is more than expected value to be earned by sellling hot dogs i.e. $50

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.