A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts thelot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at randomand without replacement from the lot is less than or equal to 1. The operating characteristiccurve is defined as the probability of accepting the lot, namelyOC (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 hypergeometricdistribution.(b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 andp = 0.16.(c) Plot, using R, the operating characteristic curve for N₁ = 1 to N₁ = 4.

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Answered: (a) Show that the probability of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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(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. (c) Plot, using R, the operating characteristic curve for N₁ = 1 to №₁ = 4.