Question

1. 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.

a. ? =_________ [5pts]

x   P(x)

0   0.12

1   0.14

2   0.25

3   0.15

                                                  4     ?

5 0.10

6   0.09

b. P(x <3) = _______

c. P(x ≥ 4) = _______  

d. On average, how long would you expect a new hire to stay with the company? ____________

Answer 1

Solution-A:

total probbailty=1 for discrete probbaility distribution

0.12+0.14+0.25+0.15+?+0.0.09=1

?=1-0.85

?=0.15

?=0.15

b. P(x <3) =

P(X=0)+P(X=1)+P(X=2)

=0.12+0.14+0.25

= 0.51

0.51

c. P(x ≥ 4) =

P(X=4)+P(X=5)+P(X=6)

=0.15+0.10+0.09

= 0.34

0.34

. On average, how long would you expect a new hire to stay with the company?

mean=sum(xP(X=x))

mean=2.73