Problem 119

Given information

Given, a manufacturer of Christmas tree light bulbs knows that 3% of its bulbs are defective. Then we have to find the probability that a string of 100 lights contains at most four defective bulbs using both the binomial and Poisson distributions. 

Step-by-step explanation

First, we find the probability that a string of 100 lights contains at most four defective bulbs using the binomial distribution.

According to the given information,3% of bulbs are defective i.e p=0.03 and the total number of bulbs are 100 i.e n=100

So ~  

PDF of Binomial distribution is, 

Then the probability that a string of 100 lights contains at most four defective bulbs will be