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what is the probability that, at the end of a period, at least 88 components are working

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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Question

A system is made up of 100 components, each of which has a reliability (probability of working properly over a period of time) equal to 0.9. In that
context, what is the probability that, at the end of a period, at least 88 components are working? (Do not use continuity correction in the approximation of the Binomial distribution by the Normal distribution.)

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Expert Solution

Step 1

Let , X be the number of components are working

Here , X→B(n=100 , p=0.9)

The probability mass function of X is ,

$P (X = x) = (\binom{n}{x}) p^{x} q^{n - x}$ ; x=0,1,2,.......,n and q=1-p

= 0 ; otherwise

Our aim is to find the probability that, at the end of a period, at least 88 components are working.

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