試題詳解

69. Let X and Y be the number of hours that a randomly selected person watches movies and sporting events, respectively, during a three-month period. The following information is known about X and Y:

E(X) = 50, E(Y) = 20, Var(X) = 50, Var(Y) = 30, Cov(X,Y) = 10.

 The totals of hours that different individuals watch movies and sporting events during the three months are mutually independent.

 One hundred people are randomly selected and observed for these three months. Let T be the total number of hours that these one hundred people watch movies or sporting events during this three-month period.

 Approximate the value of P[T ＜ 7100].
(A) 0.62
(B) 0.84
(C) 0.87
(D) 0.92
(E) 0.97