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Chapter 4: Q. 1 (page 282)

Use the following information to answer the next five exercises: A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.

Let X = the number of years a new hire will stay with the company.

Let P(x) = the probability that a new hire will stay with the company x years.

Complete Table 4.20 using the data provided.

Short Answer

Expert verified

P(4)=0.10

Step by step solution

01

Given information

A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.

Let X = the number of years a new hire will stay with the company.

Let P(x) = the probability that a new hire will stay with the company x years.

02

Explanation

if you sample N new hires (where N is large > 1000), the mean number of years they stay would be approx 2.43 (this is following the Law of large numbers). that is,

mean=0+1+2+3+5+67=2.43

Therefore the expected value of P(4)is calculated as

0×0.12+1×0.18+2×0.30+3×0.15+4×P(4)+5×0.10+6×0.05=2.432.03+4×P(4)=2.43P(4)=2.43-2.034P(4)=0.10

xP(x)
00.12
10.18
20.3
30.15
40.1
50.1
60.05

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