A lot of parts contains 500 items, 100 of which are

Chapter 4, Problem 12E

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QUESTION:

A lot of parts contains 500 items, 100 of which are defective. Suppose that 20 items are selected at random. Let X be the number of selected items that are defective.

a. Express the quantity P (X = 5) using factorials.

b. Use the binomial approximation to compute an approximation to P (X = 5).

Questions & Answers

QUESTION:

A lot of parts contains 500 items, 100 of which are defective. Suppose that 20 items are selected at random. Let X be the number of selected items that are defective.

a. Express the quantity P (X = 5) using factorials.

b. Use the binomial approximation to compute an approximation to P (X = 5).

ANSWER:

Answer:

Step 1 of 3:

Given, we have a lot of  500 items, in that 100 are defectives and 20 items are chosen at random to be tested.

Let X = number of selected items that are defectives.

Let X follows Hypergeometric distribution with probability mass function is

P(x) =   

X~H(500, 100, 20).

From the given problem, N = 500, K = 100 and n = 20


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