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2. If Y = the number of classes taken in the previous semester, what is the domain of Y ?
3 . If Z = the amount of money spent on books in the previous semester, what is the domain of Z ?
4 . Why are X , Y , and Z in the previous example random variables?
5 . After collecting data, you find that for one case, z = –7. Is this a possible value for Z ?
6 . What are the two essential characteristics of a discrete probability distribution?
Use this discrete probability distribution represented in this table to answer the following six questions. The university library records the number of books checked out by each patron over the course of one day, with the following result:
| x | P ( x ) |
|---|---|
| 0 | 0.20 |
| 1 | 0.45 |
| 2 | 0.20 |
| 3 | 0.10 |
| 4 | 0.05 |
7 . Define the random variable X for this example.
8 . What is P ( x >2)?
9 . What is the probability that a patron will check out at least one book?
10 . What is the probability a patron will take out no more than three books?
11 . If the table listed P ( x ) as 0.15, how would you know that there was a mistake?
12 . What is the average number of books taken out by a patron?
Use the following information to answer the next four exercises. Three jobs are open in a company: one in the accounting department, one in the human resources department, and one in the sales department. The accounting job receives 30 applicants, and the human resources and sales department 60 applicants.
13 . If X = the number of applications for a job, use this information to fill in [link] .
| x | P ( x ) | x P ( x ) |
|---|---|---|
14 . What is the mean number of applicants?
15 . What is the PDF for X ?
16 . Add a fourth column to the table, for ( x – μ ) 2 P ( x ).
17 . What is the standard deviation of X ?
18 . In a binomial experiment, if p = 0.65, what does q equal?
19 . What are the required characteristics of a binomial experiment?
20 . Joe conducts an experiment to see how many times he has to flip a coin before he gets four heads in a row. Does this qualify as a binomial experiment?
Use the following information to answer the next three exercises. In a particularly community, 65 percent of households include at least one person who has graduated from college. You randomly sample 100 households in this community. Let X = the number of households including at least one college graduate.
21 . Describe the probability distribution of X .
22 . What is the mean of X ?
23 . What is the standard deviation of X ?
Use the following information to answer the next four exercises. Joe is the star of his school’s baseball team. His batting average is 0.400, meaning that for every ten times he comes to bat (an at-bat), four of those times he gets a hit. You decide to track his batting performance his next 20 at-bats.
24 . Define the random variable X in this experiment.
25 . Assuming Joe’s probability of getting a hit is independent and identical across all 20 at-bats, describe the distribution of X .
26 . Given this information, what number of hits do you predict Joe will get?
27 . What is the standard deviation of X ?
28 . What are the three major characteristics of a geometric experiment?
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