Question

5.38. A nail manufacturer guarantees that not more than one nail in a box of 100 nails is defcctive. If, in fact, the probability of each individ ual nail being defective is p = 0.005, compute the probability that: (a) The next box of nails violates the guarantee. Use the Poisson approximation, after assuming independence. (b) The guarantee is violated at least once in the next 25 boxes.

Answer 1

5.38 Guren aotalilik e each indiidul ni O OO 5 Wsa nts in a bon are deferline. nails X No Each nail g dfestves XNBin (oo it Non and loge n I00 Amall O O05 male the alore distn Can We bineal wilk dist Povsson wilh a raramelei hu Y whene O.50 PLO.50) P X O.50 +- 2-0,,2 or nails vtolals hi guad = P (x) = 1- P(XS) -05 - 1- 05 0.9097q NO9018

Def ine y No. bexus lhich violalis h nerl 25 eus uranle in 25, ) yN Bin 25-4 34:022ニ 25c O.9018 O.0102 = (7P - Ply2 1- P(0 25 0 0102 25c 0.10 18 1 - NO.999 As)