Statistics+Probability 問題(急20)

2009-06-04 7:08 am

TastyMilk sells bottles of milk in two sizes. The amount in each bottle ,in ml ,is normally distributed with mean and variance as shown in the following table.

Small mean: 252(ml)
Large mean:1012(ml)
Small variance:4 (ml square)
Large variance:25 (ml square)

i)Find the probaility that a randomly selected large bottle will cointain an amount between 1000 and 1020ml

ii)If s small bottle and a large bottle are selected randomly, find the probaility that the total number in the two bottles will exceed 1300ml

iii)A bottle of each size is selected randomly.Find the probaility that the large bottle contains less than four times the amount in the small bottle.

THX

回答 (1)

myisland8132

2009-06-04 7:18 am

✔ 最佳答案

Small bottle X~ N(252,4)
Large bottle Y~ n(1012,25)

(I) P(1000<=Y<=1020)
=P((1000-1012)/5<=Z<=(1020-1012)/5)
=P(-2.4<=Z<=1.6)
=0.937

(ii) Let W=X+Y W~(1264,29)
P(W>1300)
=P(Z>(1300-1264)/sqrt(29))
=P(Z>6.685)
=0

(iii) P(Y<4X)
=P(Y-4X<0)
=P(Z<(0-4)/3) (Y-4X~N(4,9))
=P(Z<-1.3333)
=0.0912

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