A company makes electric motors. The probability an electric motor is defective is 0.01. What is the probability that a sample of 300 electric motors will contain exactly defective motors?
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Answer:
A company makes electric motors. The probability an electric motor is defective is 0.01. (a) So, out of 300 electric motors, the expected number of defective motors is (300)(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) (b) 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.)