that five lelis be defect-free? e distribution in Exercise 2, suppose that the l
ID: 2929624 • Letter: T
Question
that five lelis be defect-free? e distribution in Exercise 2, suppose that the lens are no defects for $20. If there is one defect, it can be retat n be sold as ist an be reworked at a co 4. Using th 4. then sold. If there are sold. If there are more than two detects, it must be scrapped sold. If there are two defects, it can be reworked at aata c 6. net revenue generated during the shift if 100 contact lenses d? with = 10 and normally distrbuted with and X is an independent random variable, also no and = 5, Find: (a) P(Y> 12 and X> 4) (b) P(Y> 12 or X> 4) 5. Suppose that Y is a normally distributed random variable (c) P(Y> 10 and XExplanation / Answer
Here I am working on question 5
a) p[ Y > 12 and X > 4]
= p [Zy > 12 - 10/2, and Zx > 4 - 5/5]
= p [Zy > 1, Zx > -0.2]
= 0.1587 * 0.5793
= 0.0919
b) p[ Y > 12 or X > 4]
= p[ Y > 12] or p[ X > 4]
= 0.1587 + 0.5793
= 0.7380
c)
p[ Y > 10 and X < 5]
= p [Zy > 10 - 10/2, and Zx < 5 - 5/5]
= p [Zy > 0, Zx < 0]
= 0.5 * 0.5
= 0.25
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