請各好心人 , 幫幫手很深的maths 問題

用戶10960

2009-11-28 9:01 pm

請請好心人 ,幫幫手
From past experience, the supervisor of a convenience store asserts that
the weekly demand for a particular kind of mineral water can be assumed
to be approximately normally distributed, with a mean of 230 bottles and
a standard deviation of 36 bottles.
a What is the probability that the mineral water will sell out in a given
week if the supervisor orders 200 bottles?
b What is the probability that more than ten bottles of the mineral
water will be left over in a given week if the supervisor orders 250
bottles?
c How many bottles should the supervisor order for a week so that the
probability of selling out is at most 15%?

回答 (1)

用戶9112

2009-11-29 2:02 am

✔ 最佳答案

(a) The probability of selling out 200 bottles mean the demand is greater than 200.
For a discrete number like the number of bottles, we can apply a continuity correction factor of 0.5
Therefore the probability is Pr(X > 199.5)
= Pr[Z > (199.5 - 230)/36]
= Pr(Z > -0.4872)
= 0.8016
(b) The probability that more than 10 bottles is left over means the demand is less than 250 -10 = 240
Pr(X < 239.5)
= Pr[Z < (239.5 - 230)/36]
= Pr(Z < 0.2639)
= 0.6041
(c) If he order n bottles and sell out, the probability is
Pr(X > n - 0.5)
= Pr[Z > (n - 0.5 - 230)/36] = 15%
= Pr[Z < (n - 230.5)/36] = 85%
Z = 1.036
Therefore (n - 230.5)/36 > 1.036
n - 230.5 > 37.31
n > 267.8
He should order at least 268 bottles

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