Question

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

$P\left(4\right)=0.10$

Step-by-step solution

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.

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,

$mean=\frac{0+1+2+3+5+6}{7}=2.43$

Therefore the expected value of $P\left(4\right)$is calculated as

$$\begin{gathered} 0\times 0.12+1\times 0.18+2\times 0.30+3\times 0.15+4\times P\left(4\right)+5\times 0.10+6\times 0.05=2.43 \\ 2.03+4\times P\left(4\right)=2.43 \\ P\left(4\right)=\frac{{\displaystyle 2.43-2.03}}{4} \\ P\left(4\right)=0.10 \end{gathered}$$

x	P(x)
0	0.12
1	0.18
2	0.3
3	0.15
4	0.1
5	0.1
6	0.05