Q of probability

Gary

2010-04-20 10:46 am

The weekly sales at a shop is a normal random variable with mean $2000 and standard deviation $200.
What is the probability that the total sales over the next 2 weeks exceeds $5000?
What is the probability that weekly sales exceed $1800 in at least 2 of the next 3 weeks?

回答 (1)

Prof. Physics

2010-04-20 4:26 pm

✔ 最佳答案

Let X and Y be the random variables of the weekly sales and sales in two weeks respectively.

X ~ N(2000 , 200^2)

Y ~ N(2000 X 2 , 2^2 X 200^2) ~ N(4000 , 400^2)

a. P(Y > 5000)

= P[z > (5000 - 4000)/400]

= P(z > 2.5)

= 0.5 - 0.4938

= 0.0062

b. P(X > 1800)

= P[z > (1800 - 2000)/200]

= P(z > -1)

= 0.5 + 0.3413

= 0.8413

P(X <= 1800)

= 1 - 0.8413 = 0.1587

So, P(at least 2 out of 3 weeks exceed $1800)

= [P(X > 1800)]^2P(X <= 1800) + [P(X > 1800)]^3

= (0.8413)^2(0.1587) + (0.8413)^3

= 0.7078

參考: Physics king

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