Question

Suppose a company that makes video game consoles samples 20 consoles for inspection. The probability a gaming console fails prior to the end of the warranty period is 0.08 and the failure of a console is independent between consoles. What type of distribution will best model the number of consoles out of the 20 that will fail prior to the end of the warranty period?

a) Poisson

b) Exponential

c) Normal

d) Binomial

** explain why an answer is correct and for the answers that you believe to be incorrect explain why they are incorrect. Be thorough

Answer 1

Ans:

Given that the failure of a console is independent between consoles and probability of failure is 0.08(there are only two outcomes i.e. failure or success),so the number of consoles out of the 20 that will fail prior to the end of the warranty period will follow Binomial distribution.

Correct option is d(Binomial)

Explanation:

A special discrete random variable is the binomial. We have a binomial experiment if ALL of the following four conditions are satisfied:

1. The experiment consists of n identical trials.
2. Each trial results in one of the two outcomes, called success and failure.
3. The probability of success, denoted p, remains the same from trial to trial.
4. The n trials are independent. That is, the outcome of any trial does not affect the outcome of the others