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(Hmong, S'ech‘rm) 1; "y \u Stat 25 Fall 2003 if
Open book, 50 minutes K» L' Note: Keep 3 decimal places in calculations and in answers. Frame your answers.
Show all work for full credit. Problem 1. (40 minutes, 40 points) A wholesaler sells blank recordable compact discs (CD—R} to a retailer by boxes of 20
discs for $5 a box. If a box has at least one defective disc, the retailer can return the
whole box to the wholesaler and get a $8 refund. Chance of a disc to be defective is
1%. The retailer just takes delivery of 15 boxes. A. What is the chance that a given box will have exactly 2 defective discs? B. What is the chance that exactly 3 boxes will have to be returned? (2. Suppose the retailer is inspecting a b0x that has 3 defective discs. The retailer has
time to check only 5 discs. If the 5 discs are chosen at random without replacement
from the box, what is the chance that the retailer wiil ﬁnd at least one defective disc?
D. What is the expected revenue of the wholesaler for the saie of the 15 boxes?
(revenue is total sale amount minus the eventual refunds) Xw an {3.0 ,3 0.06 r r _. . — x. (0.013" (0393)“ ' if PX i_'"""" } _ \ .
D9 l. ._ Jada} veganLac: F3: 1009562.? .‘_<\‘d \f' EJCIYOE (Ci'glfmd‘ m "1W3 mm. 31“?)
R= #5 — 37
W. W m 2. M2.) 59mg, : a E(><‘)+\o Problem 2. (10 minutes, 10 points)
Assembly of an optical data storage product requires optical alignment of the parts.
Often several trials are required before a good alignment is obtained. Chance ofa
successful alignment is 0.9. Assume trials are independent.
.05 A. What is the probability that the ﬁrst successful alignment requires exactly 4 trials?
/ B. What is the probability that the ﬁrst successful alignment requires at least 4 trials? 1 C'.\‘ — 7 "
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 Fall '05
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