A company is producing christmas light strings containing 20 small bulbs. Suppose the success or failure of a bulb is independent of the success or failure of other bulbs and the probability that a bulb is lightning properly is 0.92. a. When you order a christmas light string, what is the probability of at most 3 of those small bulbs are not lightning properly.
b. Find the mean and the variance of bulbs in a string that are not lightning properly.

Explanation:

Number of bulbs = 20

Success of a bulb lightning properly = 0.92

Success of a bulb not lightning properly = 0.08

We have to find the probability of atmost 3 bulbs not lightning properly -

The random Variable X follows binomial distribution

= 0.929385

Mean and variance of bulbs in a string that are not lightning properly is given by

Mean of binomial distribution or E(X) = n*p = 20*0.08 = 1.6

Variance of binomial distribution or V(X) = n*p*(1-p) = 20*0.08*0.92 = 1.472

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