Q. 1 Use the following information to... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

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

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,

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

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

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