elementary statistics

NAME __________________ MATH 175

Choose the most appropriate answer. Each is worth 2 points.

1. Bag 1 contains a red, white, and green ball. Bag 2 contains the numbers 1 and 2. If a ball is drawn from Bag 1 and then a number is drawn from Bag 2, there would be 6 possible outcomes. A) True B) False

2. In finding the number of possible arrangements, if order is important, then you are looking for a ___________. A) Combination B) Permutation C) Probability

3. If all events in a sample space are equally likely to occur, then, what type of probability rule would be used? A) Classical B) Empirical C) Subjective

4. A geologist says that there is a 30% chance of hitting oil at a given location. This would be what type of probability? A) Classical B) Empirical C) Subjective

5. Consider an experiment with n possible outcomes. If all the events are mutually exclusive, the product of the probabilities is equal to 1. A) True B) False

6. If A and B are two __________ events, the probability of them both occurring is zero. A) equally likely B) conditional C) independent D) mutually exclusive

7. When graphing a probability distribution, the frequency is plotted on the y axis. A) True B) False

8. The binomial distribution is an example of a distribution of a discrete variable. A) True B) False

9. The sum of the probability of an event occurring, and the probability of the event not occurring equals 1. A) True B) False

10. A probability value can only take on values between 0 and 100%.

A) True B) False

11. A point of interest that is greater than the mean will always yield a positive z – score. A) True B) False

12. A point of interest that is less than the mean will always yield a negative area under the curve of the standardized normal distribution. A) True B) False

13. The tails of the standardized normal distribution extend infinitely along the x-axis. A) True B) False

14. The area under the curve of the standardized normal distribution is equal to infinity.

A) True B) False

15. The central limit theorem assures us that the distribution of sample means resulting from sampling from a nonnormally distributed population will be approximately normally distributed, provided the sample size is sufficiently large. A) True B) False

PROBLEM SOLVING SECTION – EACH PROBLEM WORTH 10 POINTS SHOW ALL WORK

1. A) A new car buyer has a choice of the following car types: sedan, two-door, SUV, and mini-van; he also has the choice of engine types: v-6, v-8, and finally the color: red, blue, black, white, green, beige, gray. How many different cars are available from which to choose?

B) Six people are going to win $100 shopping sprees at Giant Eagle. If there are 20 that have made their way to the final round of the contest, how many possible ways are there to pick the winners of the shopping spree?

C) Suppose out of 6 staff members at a hospital, two are chosen to be team leader and assistant. How many possible ways are there to pick this pair?

2. The following table gives the results of a Gallup Poll conducted during a phone survey:

Republican Democrat Independent

18 – 29 241 351 409

A

G 39 – 49 299 330 370

E

S 50 – 64 282 341 375

65+ 279 382 343

If a person is selected at Random, find the probability that:

A) He/she is either a Democrat or a Republican

B) He/she is either a Democrat or is 18 – 29 years old.

C) He/she is 50 years or older.

D) He/she is less than 18 years old.

3. There is going to be a council of students put together to help with making decisions on how money should be spent from student government. There are 4 freshman, 6 sophomores, 7 juniors and 3 seniors interested in helping with this project. How many ways are there of forming a committee of 6 students if the following conditions must be met?

a) 1 freshman, 2 sophomores, 2 juniors, and 1 senior

b) 0 freshmen, and two of each of the other classes

c) three freshmen, three seniors and no sophomores or juniors

3. A probability distribution was developed to indicate the number of cartoons watched by first graders on a Saturday morning. It is shown below:

# of cartoons 0 1 2 3 4 5

P(x) 0.2 0.2 0.3 0.15 _____ 0.05

a) find the probability that 4 cartoons are watched.

b) Construct a graph for the distribution

c) Find the long run average of cartoons watched by kids

d) Find the variance and standard deviation

5. Suppose that 30% of all high school students smoke tobacco. If 15 students are selected at random, what is the probability that:

a) exactly four are smokers?

b) at most four are smokers?

c) At least three are smokers?

d) between two and seven are smokers?

e) that all fifteen are smokers?

6. In a certain city, the response times of an emergency service are approximately normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. What is the probability that the response time will be:

a) Less than 10 minutes

b) Greater than 18 minutes?

c) Between 23 and 27 minutes?

d) Between 18 and 27 minutes?

e) The slowest 14% of the calls take how long?

7. The daily sales at a surf shop are normally distributed with a mean of $1000 and a standard deviation of $200. If a random sample of 50 days is taken, find the probability that the mean sales is:

a) Greater than $1,025

b) Is between $950 and $1050

c) Is less than $1040?

d) Is between $925 and $965?

BONUS:

A statistics teacher has students that want her to grade on a curve. The mean of the exam was 78% with a standard deviation of 8%. If the top 10% of the students receive an A; the next 25% receive a B; the next 30% receive a C; the next 15% receive a D; and all else Fail, what are the cut-off scores to make this happen?

Each grade cut-off score is worth 2 points