Suppose that only 0.1% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 3,000 computers. (a) What are the expected value and standard deviation of the number of computers in the sample that have the defect? (Round your standard deviation to two decimal places.) expected value computers standard deviation computers (b) What is the (approximate) probability that more than 5 sampled computers have the defect? (Round your answer to three decimal places.) (c) What is the (approximate) probability that no sampled computers have the defect? (Round your answer to five decimal places.)

a) The mean is 3 computers and the standard deviation is 1.73 computers.

b) 0.916

c) 0.04971

Step-by-step explanation:

For each computer, there are only two possible outcomes. Either they experience failure during the warranty period, or they do not. The probability of a computer experiencing a failure is independent of other computers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

In this problem we have that:

(a) What are the expected value and standard deviation of the number of computers in the sample that have the defect? (Round your standard deviation to two decimal places.)

The mean is 3 computers and the standard deviation is 1.73 computers.

(b) What is the (approximate) probability that more than 5 sampled computers have the defect? (Round your answer to three decimal places.)

Either 5 or less have the defect, or more than five do. The sum of the probabilities of these events is decimal 1. So

We want P(X > 5).

So

(c) What is the (approximate) probability that no sampled computers have the defect? (Round your answer to five decimal places.)