Question

A) Suppose that the number of visits to a certain website during a fixed interval follows a Poisson distribution. Suppose that the average of the visit ratio is five in each minute. What is the probability that there are only 17 visits in the next three minutes?

POSSIBLE ANWERS FOR A: a.- 0.0847 b.- 0.0145 c.- 0.2345 d.- 0.0897

B) In a lottery, 10,000,000 tickets are sold for a raffle with 100 prizes. How many lottery tickets must be purchased so that the probability of winning at least one prize is equal to 0.10?

POSSIBLE ANWERS FOR B: a.- 10536.1 b.- 120236 c.- 105361 d.- 100

C) An electronic company observes that the number of components that fail before reaching 100 hours of operation is a Poisson random variable. If the average number of these failures is eight. What is the probability that no more than three components fail in 50 hours?

POSSIBLE ANWERS FOR C: a.- 0.5665 b.- 0.9576 c.- 0.0423 d.- 0.4334

D) The average number of accidents that occur weekly on a given highway is 2. Calculate the probability of more than 3 accidents occurring in two consecutive weeks.

POSSIBLE ANWERS FOR D: a.- 0.567 b.- 0.762 c.- 0.195 d.- 0.238

E) Two batteries are randomly selected from a box containing 12, of which 8 are good and 4 are defective. What is the expected number of defective batteries selected?

POSSIBLE ANSWERS FOR E: a.- 2 b.- 3/5 c.- 4 d.- 8/12

Answer 1

A) The Poisson PMF is

For next three minutes , the Poisson parameter is

Correct choice is (A).

B) Probability of win of a lottery ticket is . Use Binomial distribution,

We need such that

Correct choice is (A).

C) The required probability is

Correct choice is (C).

D)For next 2 consecutive weeks , the Poisson parameter is

The required probability is

Correct choice is (A).

E) This is Binomial trials, expectation of Binomial random variable is

Correct choice is (C).