Suppose the following data represent the number of persons unemployed for a given number of months in Killeen, Texas. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons.

Months Number

Unemployed                Unemployed

1 .............................................. 1,029

2 ..............................................1,686

3 ..............................................2,269

4 ..............................................2,675

5 ..............................................3,487

6 ..............................................4,652

7 ..............................................4,145

8 ..............................................3,587

9 ..............................................2,325

10 .............................................1,120

Let x be a random variable indicating the number of months a randomly selected person is unemployed.

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 person is unemployed for two months or less? Unemployed for more than two months?

d. What is the probability that a person is unemployed for more than six months?