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Chapter 4: Q.4.28 (page 165)

A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.

Short Answer

Expert verified

The expected number of defective items in the sample isEX=0.6

Step by step solution

01

Given Information

Xis the random variable which denotes the number of items in the sample.

we selected 3 items for sample ,then we can assume the value of Xis 0,1,2,3

probability of Xis kk

02

Explanation

Here,

P(X=k)=4k·163-k203

Using the formula for expectation,we have that

E(X)=∑k=03k·P(X=k)=∑k=03k·4k·163-k203

=12031·41·162+2·42·161+3·43·161

=0.6

03

Step 3:Final Answer

The expected number of defective items in the sample isEX=0.6

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In Example 4b, suppose that the department store incurs an additional cost of cfor each unit of unmet demand. (This type of cost is often referred to as a goodwill cost because the store loses the goodwill of those customers whose demands it cannot meet.) Compute the expected profit when the store stocks s units, and determine the value of data-custom-editor="chemistry" s that maximizes the expected profit.

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