Question

# The number of home runs in a baseball game is assumed to have a Poisson distribution...

The number of home runs in a baseball game is assumed to have a Poisson distribution with a mean of 3. As a promotion, a company pledges to donate \$10,000 to charity for each home run hit up to a maximum of 3. Find the expected amount that the company will donate. Another company pledges to donate C for each home run over 3 hit during the game, and C is chosen so that the second company's expected donation is the same as the first. Find C.

Let X be the random variable denoting the number of home runs in a baseball game.

X ~ Poi(3).

We have, P(X 3) = = 0.6472

The expected amount that the company will donate = \$10,000 * 0.6472 = \$6472 (Ans).

The probability that a home run over 3 hit during the game = P(X > 3) = 1 - P(X 3) = 1 - 0.6472 = 0.3528

The expected amount another company will donate = \$C * 0.3528

Given that, 0.3528 C = 6472 i.e. C = \$18,345 (approximately) (Ans).

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