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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
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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