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

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