Short Answer

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.

$P (4) = 0.10$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

Step 2: 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,

$m e a n = \frac{0 + 1 + 2 + 3 + 5 + 6}{7} = 2.43$

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

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

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

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