Question

a firm sells four items randomly selected from a large lot that is known to contain 12% defectives. let x denote the number of defectives among the four sold. the purchaser of the items will return the defectives for repair, and the repair cost is given by c

Answer 1

The student's question involves calculating the probability distribution for the number of defective items among four sold, given a 12% defect rate using binomial distribution.

Step-by-step explanation:

The question is related to the field of probability and involves the concept of binomial distribution, which is used to model the number of successes in a fixed number of trials performed under the same conditions. In this scenario, we are given that a firm sells four items and we're interested in finding the probability distribution for the number X of defective items in those four, knowing that there is a 12% chance for any item to be defective.

This situation assumes a binomial distribution X ~ B(n, p), where n is the number of trials (items selected), which is 4, and p is the probability of success (finding a defective item), which is 0.12.

For a random variable X, which is defined as the number of defectives among the four, probabilities of X taking on values from 0 to 4 can be calculated using the binomial distribution formula:

P(X = x) = C(n, x) * p^x * (1-p)^(n-x),

where C(n, x) is the combination of n items taken x at a time. Related to the student's question, if the defective items are returned for repairs, understanding this distribution helps calculate the expected repair cost, denoted by c.