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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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A batch contains 36 bacteria cells and 12 of the cells are

Chapter 3, Problem 144E

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QUESTION:

A batch contains 36 bacteria cells and 12 of the cells are not capable of cellular replication. Suppose that you examine three bacteria cells selected at random without replacement.

(a) What is the probability mass function of the number of cells in the sample that can replicate?

(b) What is the mean and variance of the number of cells in the sample that can replicate?

(c) What is the probability that at least one of the selected cells cannot replicate?

Questions & Answers

QUESTION:

A batch contains 36 bacteria cells and 12 of the cells are not capable of cellular replication. Suppose that you examine three bacteria cells selected at random without replacement.

(a) What is the probability mass function of the number of cells in the sample that can replicate?

(b) What is the mean and variance of the number of cells in the sample that can replicate?

(c) What is the probability that at least one of the selected cells cannot replicate?

ANSWER:

Step 1 of 5

Given,

Number of bacteria, N = 36

Objects classified as successes,

Sample size, n = 3

The random variable X that equals the number of successes in the sample is a

hypergeometric random variable and the probability mass function is,

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