c. What is the appropriate distribution to model this problem? (2) You volunteer

Question

c. What is the appropriate distribution to model this problem? (2) You volunteer to be in charge of ordering shirts for Camp War Eagle for next summer. The person who was in charge last year gives you the following information about t distribution of shirt orders from 2017, where X is the number of shirts that might have been needed in 2017. 8. he E[X]- 5,500 Var(X) = 2,500 neede After meeting with the admissions office, you conclude that the number of shirts for next year is 1.5 times higher than what you needed last year, and you are going to order an extra 300 shirts on top of that. Let Y be the number of shirts that you might need for Camp War Eagle in 2018. a. Write and expression relating X and Y (write Y in terms of X). (2) b. What is E[Y]? (2) c. What is Var[Y]? (2) d. What is EY](2)

Explanation / Answer

Here, X = number of shirts needed in 2017 Camp War Eagle

and Y = number of shirts might be needed in 2018 Camp War Eagle

Given that, the number of shirts might be needed is 1.5 times higher than last year and I will order 300 shirts on top of that.

a) Therefore, we get the relationship as,

Y = 1.5*X + 300

So,

b) E(Y) = 1.5*E(X) + 300 = 1.5*5500 + 300 = 8550

c) V(Y) = 1.52 * V(X) = 2.25 * 2500 = 5625

d) E(Y2) = V(Y) + (E(Y))2 = 5625 + 85502 = 73108125

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