1. Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a)
Find n(A).
n(A) =
(b) True or false: 26
A
-True
-False
(c) True or false: 2 A
-True
-False
(d) True or false: 14 A
-True
-False
2.
The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
If A = {0, 3, 6, 8} and B = {0, 1, 6, 9}, find the following. (Enter your
answers as a comma-separated list. Enter EMPTY for the empty set.)
(a) A ∩ B
{_________}
(b) A ∪ B
{________}
(c) A’
{________}
(d) B’
{_________}
3. In a recent health survey, 700 single men in their twenties were asked to check the appropriate box or boxes on the following form.
The results were tabulated as follows: 343 men checked the gym box, 105 checked the vegetarian box, and 314 were blank (no boxes were checked).
(a) In the following Venn diagram, Region G represents single men who are members of a private gym and Region V represents single men who are vegetarians. Determine each value on the Venn diagram. (Enter 0 for any empty subset.)
Outside left of circles: U
Left circle: G
Right circle: V
(b)
What percent of these men were both members of a private gym and vegetarians?
(Round your answer to one decimal place.)
_______%
4. To study the eating habits of students at a local college, thirty randomly selected students were surveyed to determine the number of times they had purchased food at the school cafeteria during the last week. The following results were obtained.
| 4 | 3 | 1 | 2 | 3 | 3 | 3 | 3 | 2 | 5 |
| 3 | 1 | 1 | 3 | 1 | 2 | 1 | 1 | 1 | 2 |
| 1 | 2 | 2 | 2 | 4 | 5 | 2 | 5 | 4 | 4 |
(a) Organize the given data by creating a frequency distribution.
| Number of Times Purchased Food | Frequency |
| 1 | _______ |
| 2 | _______ |
| 3 | _______ |
| 4 | _______ |
| 5 | _______ |
(b) Construct a pie chart to represent the data. Choose
one.
| |
(c) Construct a histogram using single-valued classes of
data. Choose one.
5. The following table lists some common specialties of physicians in the United States in a certain year.
| Specialty | Male | Female |
| Family Practice | 54,028 | 26,303 |
| General Surgery | 32,347 | 5,163 |
| Internal Medicine | 104,643 | 46,212 |
| Obstetrics/Gynecology | 24,806 | 17,288 |
| Pediatrics | 33,529 | 36,635 |
| Psychiatry | 27,215 | 13,056 |
(a) Construct a pie chart to represent the male data.
| |
(b) Construct a pie chart to represent the female data.
| |
(c) Compare the results of parts (a) and (b). What
conclusions can you make? (Select all that apply.)
A higher percentage of females than males are general surgeons
A higher percentage of females than males are pediatricians.
A higher percentage of males are general surgeons than practice internal medicine.
A higher percentage of females are general surgeons than practice psychiatry.
A higher percentage of males than females are pediatricians.
A higher percentage of males than females are general surgeons.
(d) Construct a pie chart to represent the total data.
Choose one.
6. The frequency distribution shown in the following table lists the number of hours per day a randomly selected sample of teenagers spent watching television. Where possible, determine what percent of the teenagers spent the following number of hours watching television. (Round your answers to one decimal place. If not possible, enter IMPOSSIBLE.)
| Hours per day | Number of Teenagers |
| 0 ≤ x < 1 | 17 |
| 1 ≤ x < 2 | 32 |
| 2 ≤ x < 3 | 23 |
| 3 ≤ x < 4 | 39 |
| 4 ≤ x < 5 | 26 |
| 5 ≤ x < 6 | 12 |
| 6 ≤ x < 7 | 15 |
(a) less than 4 hours
(No Response) %
(b) at least 5 hours
_____%
(c) at least 1 hour
_____%
(d) less than 2 hours
_____%
(e) at least 2 hours but less than 4 hours
_____%
(f) more than 3.5 hours
_____%
7. Erica has her savings in a bank account
that pays 5.5% interest per year. She is
considering buying stock in a pharmaceuticals company that is developing a cure
for cellulite. Her research indicates that she could earn 45% in one year if the cure is successful or lose 50% in one year if it is not. At what probability of success
would the pharmaceuticals stock be the better choice? (Round your answer to two
decimal places.)
probability ≥ _____
8. A group of twenty-four people is selected at random. What is the probability that at least two of them will have the same birthday? (Round your answer to four decimal places.)
_____
9. You order eighteen burritos to go from a Mexican restaurant, nine with hot peppers and nine without. However, the restaurant forgot to label them. If you pick four burritos at random, find the probability of the given event. (Round your answer to three decimal places.)
Exactly one has hot peppers.
_____
10. Two hundred people apply for three jobs. Eighty of the applicants are women.
(a) If three people are selected at random,
what is the probability that all are women? (Round your answer to six decimal
places.)
_____
(b) If three people are selected at random, what is the
probability that two are women? (Round your answer to six decimal places.)
_____
(c) If three people are selected at random, what is the
probability that one is a woman? (Round your answer to six decimal places.)
_____
(d) If three people are selected at random,
what is the probability that none is a woman? (Round your answer to six decimal
places.)
_____
(e) If you were an applicant, and the three selected
people were not of your gender, should the above probabilities have an impact
on your situation? Why? Choose one.
-The probabilities do not indicate presence or absence of gender discrimination. For the employer to choose the most appropriate person for the job means that not all events are equally likely.
-Yes, the probabilities indicate the presence of gender discrimination.
-No, the probabilities do not indicate the presence of gender discrimination because in the hiring process all outcomes are equally likely.
11. If o(E) = 5:9, find o(E’).
o(E’) = _____
12. Asthma, chronic bronchitis, and emphysema are conditions associated with obstructive lung disease (OLD), a leading cause of morbidity and mortality worldwide. A survey of 937 obstructive lung disease patients reveal that 212 had chronic bronchitis and 312 had emphysema. Of the 312 emphysema patients, 102 had chronic bronchitis. How many patients had asthma? Choose one.
-523
-515
-517
-527
13.Medication errors in a hospital can be dangerous and expensive. Medication errors are defined as giving a patient a non-prescribed medication in any quantity or the improper dosage of a prescribed medication. Suppose the national average for medication error is one out of every 1000 patients. A hospital believes that their medication error rate is comparable to the national average. If the hospital randomly selects 500 patients, find the expected number of patients in the sample that will have had a medication error.
______
14. There are 4 known blood types among all the people of our planet: A, B, AB, and O. Type O represents approximately 50% of the population and type AB represents approximately 2% of the population. Find the probability that a person has O or AB blood type. Write your answer either in decimal or in fraction.
______
15. A couple is facing the risk that their children may suffer from a genetic disorder, because both the husband and the wife are known to be heterozygote (Aa) carriers of the harmful recessive allele a (the homozygote aa individuals are affected by the disorder, all others are healthy). The couple plans to have two children, and wants to know the prospects for their health: What is the probability that both children will be healthy? Write your answer in two decimal places.
______
16. A committee of four is to be selected from a group of fifteen people. How many different committees are possible, given the following conditions?
(a) There is no distinction between the
responsibilities of the members.
_____
(b) One person is the chair, and the rest are general
members.
_____
(c) One person is the chair, one person is the secretary,
one person is responsible for refreshments, and one person cleans up after
meetings.
_____
17. A group of eight women and four men must select a four-person committee. How many committees are possible if it must consist of the following?
(a) two women and two men
_____
(b) any mixture of men and women
(_____
(c) a majority of women
_____
18. Use the data in the table below to complete the exercise. Round off your answers to a tenth of a percent.
Blood types per 100 people.
| Blood Type | O+ | O− | A+ | A− | B+ | B− | AB+ | AB− |
| Occurrence | 39 | 8 | 28 | 5 | 11 | 3 | 4 | 2 |
Of all the people who have type A blood, what percent are the following?
(a) Rh positive
_____%
(b) Rh negative
_____%
