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Question
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are find the mean and variance
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Solution
Probability of getting a defective item
p = `5/100 = 1/20`
q = 1 – p
⇒ q = `1 - 1/20`
= `(20 - 1)/20`
q = `19/20` and n = 10
In binomial distribution
P(X = x) = nCxpxqn-x
Here (X = x)= `10"C"_x (1/20)^x (19/20)(10 - x)`
Mean E(x) = np
= `10 xx 1/20`
= `1/2`
= 0.5
Varaince = npq
= `10 xx 1/20`
= `19/20`
= `19/40`
= 0.475
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