Question

It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A grocery store purchases a random sample of 100 frozen chickens. a. What is the probability that the store will have at least 20 contaminated chickens? b. On average, how many contaminated chickens will be in the sample of 100 chickens? Must be answered with minitab express.

Answer 1

Concepts and reason

A Binomial experiment is a probability experiment that satisfied the following assumptions:

There must be fixed number of trials.

Each trial can have only two outcomes or outcomes that can be reduced to two outcomes.

These outcomes can be considered as either success or failure.

The outcome of each trial must be independent of one another.

The probability of success must remain the same for each trial.

Fundamentals

The probability density function of the Binomial distribution is,

Here, denote the sample size.

denote the success

denote the probability of success

a)

Calculate the probability that the store will have at least 20 contaminated chickens.

b)

Calculate the average number of chickens will be in the sample.

Ans: Part a

The probability that the store will have at least 20 contaminated chickens is 0.9911.

Part b

The average number of chickens will be in the sample is 30.