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Chapter 4: Q.5 (page 282)

What does the column 鈥�P(x)鈥� sum to?

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to

sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established

a probability distribution.

Short Answer

Expert verified

The sum of the columnsP(X) is 1.

Step by step solution

01

Given Information

The column P(X)total from the table is used. A business needs to assess its attrition rate, or how long new employees stay with the organization.

They've developed the following probability distribution over time.

02

 Concept Used

Let's defineXthe number of years a new hire will stay with the company P(X)and the probability of staying with the company forX years.

The probability mass function of a discrete variable is P(X)and the probability mass function of a discrete variable Xonly when,

i. P(X)鈮�0for all X

ii.鈭�P(X)=1

03

Calculation

The column sum can be calculated using condition (ii) as:

鈭�P(X)=0.12+0.18+0.30+0.15+0.10+0.10+0.05=1

04

Conclusion:

As a result, the sum of the columns P(X)is 1.

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Most popular questions from this chapter

A group of Martial Arts students is planning on participating in an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration.

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