If 90% of the parts produced by a certain machine do not are not defective and which are chosen at random and with discount 25 pieces in production, what is the probability that at least 22 of these parts are functional (non-defective)? Calculate the expectation and variance of the number of non-defective parts.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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If 90% of the parts produced by a certain machine do not
are not defective and which are chosen at random and with
discount 25 pieces in production, what is the probability
that at least 22 of these parts are functional (non-defective)? Calculate the expectation and variance of the number of
non-defective parts.

Expert Solution
Step 1: Information given is

Probability of the parts produced by a certain machine are not defective(p)=0.90

sample size(n)=25

Let "x" be the no. of parts are functional(not defective)

x~Binomial(n=25,p=0.90)

P(X=x)=open parentheses table row straight n row straight x end table close parentheses cross times straight p to the power of straight x cross times left parenthesis 1 minus straight p right parenthesis to the power of straight n minus straight x end exponent space space space semicolon space straight x equals 0 comma 1 comma... comma straight n


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