## Question

###### A company makes electric motors. The probability an electric motor is defective is 0.01.So, out of 300 electric motors, the expected number of defective motors is 300 X 0.01 3. With this in mind, use a Poisson distribution to estimate the probability that exactly 5 motors are defective: (Use at least 5 decimal places)Notice that; if we are assuming that the defectiveness of each motor is independent from the others, then the number of defective motors out of the 300 should follow a Binomial dist

A company makes electric motors. The probability an electric motor is defective is 0.01. So, out of 300 electric motors, the expected number of defective motors is 300 X 0.01 3. With this in mind, use a Poisson distribution to estimate the probability that exactly 5 motors are defective: (Use at least 5 decimal places) Notice that; if we are assuming that the defectiveness of each motor is independent from the others, then the number of defective motors out of the 300 should follow a Binomial distribution with n 300 and p 0.01 Use this distribution to calculate the probability that exactly 5 motors are defective, and compare it with your estimate from part (a). (Again; calculate the answer to at least 5 decimal places_ (In the case where n is very large and p is very small in a Binomial distribution, the Poisson distribution is computationally easier to handle but gives good , approximations for the probabilities. This is essentially what s known as the "law of rare events"