# University of South Florida Empirical Discrete Probability Distribution Excel Task

### Question Description

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1. 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 five 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 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?

d. Compute the expected value and variance for x.

2. How Teenagers Listen to Music. For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listened to music in the past 12 months. Nearly two-thirds of U.S. teenagers under the age of 18 say they use Google Inc.s video-sharing site to listen to music and 35% of the teenagers said they use Pandora Media Inc.s custom online radio service (The Wall Street Journal). Suppose 10 teenagers are selected randomly to be interviewed about how they listen to music.

a. Is randomly selecting 10 teenagers and asking whether or not they use Pandora Media Inc.s online service a binomial experiment?

b. What is the probability that none of the 10 teenagers uses Pandora Media Inc.s online radio service?

c. What is the probability that 4 of the 10 teenagers use Pandora Media Inc.s online radio service?d. What is the probability that at least 2 of the 10 teenagers use Pandora Media Inc.s online radio service?

3. Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.

a. What is the probability that a Dutch male is shorter than 175 cm?

b. What is the probability that a Dutch male is taller than 195 cm?

c. What is the probability that a Dutch male is between 173 and 193 cm?

d. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?