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A lab orders a shipment of 100 rats a week, 52 weeks a year,

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A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution found in Figure E:
price: 10.00, 12.50, 15.00
probability: .3, .2, .5

How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.)

Rajeevan Pillai :

Let X denote the price of a randomly selected weekly shipment. Then X has the following probability distribution.

Price 10.00 probability 0.3

Price 12.50 probability 0.2

Price 15.00 probability 0.5

Expected price of a weekly shipment = Σ x P(x) = 10.00 * 0.3 + 12.50 * 0.2 + 15.00 * 0.5

= 3 + 2.5 + 7.5 = 13

Let X1, X2, …, X52 be the prices of the first, second,…,52nd weekly shipments next year.

Then the total budget is X1 +X2 +…+X52

The expected budget is E(X1 +X2+…+X52) = E(X1)+…+E(X52) = 13+…+13 = 13 * 52 = 676

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