Employee Retention: 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.) Consider the following example of sample data of 2000 college graduates who graduated 5 years ago.

Time with Current Employer (Years)	Number
1	506
2	390
3	310
4	218
5	576

Let x be the random variable indicating the number of years the respondent has worked for her/his 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?

2. Investing in the stock market. According to a 2017 Gallup survey, the percentage of individuals in the United States who are invested in the stock market by age is as shown in the following table (Gallup Website)

Age Range	Percent of Individuals Invested in Stock Market
18 to 29	31
30 to 49	62
50 to 64	62
65+	54

A) how many 18 to 29 year olds must be sampled to find at least 50 who invest in the stock marketon average (i.e., in expected value)?

b) how many people 65 years of age and older must be sampled to find at least 50 who invest in the stock marketon average (i.e., in expected value)?

c) If 1000 individualsaged 18 to 29 are randomly sampled, what is the expected number of people who invest in the stock market in this sample? What is the standard deviation of the number of people who invest in the stock market in this sample?

d) If 1000 individualsaged 65 and older are randomly sampled, what is the expected number of people who invest in the stock market in this sample? What is the standard deviation of the number of people who invest in the stock market in this sample?