A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the lot of N₁ + N₂ 25 bulbs if the number of defectives, X among n= 5 items taken at random and without replacement from the lot is less than or equal to 1. The operating characteristic curve is defined as the probability of accepting the lot, namely OC(p) = P(X ≤ 1) = P(X= 0) + P(X= 1), where p = N₁/25 is the probability of a bulb being defective. (a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and p = 0.16.
A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the lot of N₁ + N₂ 25 bulbs if the number of defectives, X among n= 5 items taken at random and without replacement from the lot is less than or equal to 1. The operating characteristic curve is defined as the probability of accepting the lot, namely OC(p) = P(X ≤ 1) = P(X= 0) + P(X= 1), where p = N₁/25 is the probability of a bulb being defective. (a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and p = 0.16.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the
lot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at random
and without replacement from the lot is less than or equal to 1. The operating characteristic
curve is defined as the probability of accepting the lot, namely
OC (p) = P(X ≤ 1) = P(X = 0) + P(X = 1),
where p = N₁/25 is the probability of a bulb being defective.
(a) Show that the probability of the picking exactly X defectives follows a hypergeometric
distribution.
(b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and
p = 0.16.
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