Question

# Q2)   Consider a Poisson probability distribution with λ=4.9. Determine the following probabilities. ​a) exactly 5 occurrences...

Q2)   Consider a Poisson probability distribution with λ=4.9. Determine the following probabilities.

​a) exactly 5 occurrences

​b) more than 6 occurrences

​c) 3 or fewer occurrences

Q3) Consider a Poisson probability distribution. Determine the probability of exactly six occurrences for the following conditions.

​a) λ=2.0

​b) λ=3.0

​c) λ=4.0

​d) What conclusions can be made about how these probabilities change with λ​?

Q4) A particular intersection in a small town is equipped with a surveillance camera. The number of traffic tickets issued to drivers passing through the intersection follows the Poisson distribution and averages 5.3 per month.

a. What is the probability that 5 traffic tickets will be issued at the intersection next​ month?

b. What is the probability that 3 or fewer traffic tickets will be issued at the intersection next​ month?

c. What is the probability that more than 6 traffic tickets will be issued at the intersection next​ month?

Q5) A customer support center for a computer manufacturer receives an average of 2.6 phone calls every five minutes. Assume the number of calls received follows the Poisson distribution.

a. What is the probability that no calls will arrive during the next five​ minutes?

b. What is the probability that 3 or more calls will arrive during the next five​ minutes?

c. What is the probability that 3 calls will arrive during the next ten​ minutes?

d. What is the probability that no more than 2 calls will arrive during the next ten​ minutes?

Q6) Production records indicate that 3.3% of the light bulbs produced in a facility are defective. A random sample of 35 light bulbs was selected.

a. Use the binomial distribution to determine the probability that fewer than three defective bulbs are found.

b. Use the Poisson approximation to the binomial distribution to determine the probability that fewer than three defective bulbs are found.

c. How do these two probabilities​ compare?

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