Question

9. Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for their current employer (Bureau of Labor Statistics website, December 2015). Consider the following example of sample data of 2000 college graduates who graduated five years ago. Number Time with Current Employer (years) 506 390 310 218 576 Let x be the random variable indicating the number of years the respondent has worked for her/his current employer a. Use the data to develop an empirical discrete probability distribution for x. b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution c. What is the probability that a respondent has been at her/his current place of employment for more than 3 years?

Answer 1

Solution:

Discrete probability distribution can be written as follows

X. Number P(X)

1 . 506 (506/2000) = 0.253

2 390 (390/2000) = 0.195

3 310 (310/2000) = 0.155

4 218 (218/2000) = 0.109

5 576 (576/2000) = 0.288

Solution(b)

For valid discrete probability distribution total probability should be 1

P= 0.253+0.195+0.155+0.109+0.288 = 1

So it is a discrete probability distribution.

Solution(c)

Probability for more than 3 years = p(X=4) + P(X=5) = 0.109+0.288 = 0.397 or 39.7%