(20 points ) statistics

2009-11-21 6:20 pm

求教及步驟　謝謝

from past experience the supervisor of a convenience store asserts that the weekly damand for a particular kind of mineral water can be assumed to be approximately normally distributed ,with mean of 230 bottles and a standard deviation of 36 bottles

1. what is probability that the mineral water will sell out in given week if the supervisor orders 200 bottles?

2.what is probability that more than ten bottles of the mineral water will be left over in a given week if the supervisor orders 250 bottles?

3.how many bottles should the supervisor order for week so that the probability of selling out is at most 15%?

回答 (1)

用戶9112

2009-11-21 8:30 pm

✔ 最佳答案

(1) First of all since number of bottles is a discrete number while normal distribution is a continuous distribution, we have to apply a continuity correction factor of 0.5 in the calculation.
http://en.wikipedia.org/wiki/Continuity_correction
For selling out of 200 bottles, it means the demand is at least 200 bottles.
Pr(x > 199.5)
= 1 - Pr(x <= 199.5)
= 1 - Pr[z <= (199.5 - 230)/36]
= 1 - Pr(z <= -0.8472)
= 0.8016
(2) Ordering 250 bottles leaving more than 10, means the demand is less than 240
Pr(x < 239.5)
= Pr[z < (239.5 - 230)/36]
= Pr(z < 0.2639)
= 0.6041
(3) The probability of selling out <= 15% means probability of demand less than supply is 85%
Pr(z < zo) = 0.85 => zo = 1.036
xo = 230 + 1.036 * 36 = 267.3 < 267.5
268 bottles should be ordered.

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