Probability And Statistical Methods For Engineers Worksheets With Answer Key - Mae 108, 2011 Page 3
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4(3) (10 points)
The weekly demand for a product has a normal distribution with with mean 1,000 and standard
deviation 200. Assume that the demands in different weeks are independent.
(a) What is the probability that the demand next week is less than 1,100?
We use the Φ formula seen in class:
1, 100
1, 000
P (D < 1, 100) = Φ
0 = Φ(1/2)
69.1%
200
using the table in Appendix A.
(b) What is the probability that the demand in each of the next four weeks is above 800?
For each week, the demand to be above 800 is
800
1, 000
P (D > 800) = 1
P (D
800) = 1
Φ
= 1
Φ ( 1)
200
and we have seen in class that Φ ( 1)+Φ (1) = 1 thus P (D > 800) = Φ(1) = 84.1%. The probability
4
that this be true in each of the next 4 weeks is thus P = Φ(1)
50% by statistical independence.
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