For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. 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 .............                1029

2 .............                1686

3 .............                2269

4 .............                2675

5 .............                3487

6 .............                4652

7 .............                4145

8 .............                3587

9 .............                2325

10 .............              1120

Let x be a random variable indicating the number of months a 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?