Question

If the Jiffy Oil service rate for changing the oil in passenger cars is seven cars per hour. What is the probability that in the next hour four car will be serviced? (This is a Poisson Binomial Event) What is the probability that in the next hour, more than four car will need their oil changed?

Answer 1

Solution: We are given that the service rate for changing the oil in passenger cars is seven cars per hour. Therefore, the random variable follows the Poisson distribution with mean 7. Therefore, we have:

What is the probability that in the next hour four car will be serviced?

Answer: We are required to find here:

Using the Poisson distribution model, we have:

  

Therefore, the probability that in the next hour four cars will be serviced is 0.0912

What is the probability that in the next hour, more than four cars will need their oil changed?

Answer: We are required to find here:

We know that:

Therefore, the probability that in the next hour, more than four cars will need their oil changed is 0.8270