Math.... Due in 6H

Math 109 Final Exam Study Guide Name ____________________________

1. Perform the indicated operations given that: U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 7, 8, 9}, B = {1, 2, 5, 8}, and C = {3, 5}

a. A’ b. A ∩ C c. A ∩ B d. A ∪ C e. B’ ∩ C

2. A travel agent surveyed 100 people to find out how many of them had visited the cities of New York and Chicago. Thirty-one people had visited New York, 26 people had visited Chicago, and 45 people had visited New York or Chicago.

a. Complete the Venn Diagram

b. How many people had been to New York and Chicago?

c. How many people had been to New York only?

d. How many people had been to neither city?

3. If there are thirteen students in a class, in how many ways can a team of 3 be selected?

4. How many different meals can be made from two kinds of meat, five vegetables, four fruits, and seven desserts if a meal consists of one selection from each group?

5. How many ways can a teacher award 1st, 2nd, 3rd, and 4th place prizes to 4 of her students if all 25 students are eligible?

6. A group of 6 men and 8 women must select a committee of three people. How many committees are possible if the committee must consist of two men and one woman?

7. If 13

4 )( Ep , find o(E) and o(E’).

8. If a single marble is randomly chosen from a jar containing 2 blue marbles, 4 red marbles, and 5 yellow marbles, find each of the following:

a. the odds in favor of choosing a red marble

b. the odds in favor of choosing a yellow marble

c. the odds against choosing a blue marble

d. the probability of choosing a blue marble

9. Five cards are chosen at random from a standard deck. Find the probability that exactly 2 cards are clubs.

10. Two cards are dealt from a standard deck of 52 cards, one right after the other. a. Find the probability that the first card dealt is a queen. b. Find the probability that the second card is a queen given that the first card is a queen. c. Find the probability that the first card is a queen and the second card is a queen.

11. A survey of middle school students asked: What is your favorite winter sport? The results are

summarized below:

Grade Snowboarding Skiing Ice Skating TOTAL 6th 68 41 46 155 7th 84 56 70 210 8th 59 74 47 180

TOTAL 211 171 163 545

a. If a student is selected at random, what is the probability that the student will be in the 8th grade? b. What is the probability that a student’s favorite sport is skiing? c. What is the probability that a student is in the 7th grade given that the student’s favorite sport is

snowboarding? d. What is the probability that a student’s favorite sport is ice skating given that the student is in the 7th

grade?

12. The number of sales per week and the associated probabilities of a car salesman are given in the

following table. Find the expected number of sales per week.

number of sales per week

0 1 2 3 4

probability .50 .30 .10 .07 .03

13. Find the mean, median, mode, and range for the following set of data: 12, 15, 21, 34, 17, 19, 12, 23, 25, 23, 12, 9

14. Find the mean and standard deviation for the following data: 63, 70, 68, 60, 64

15. Find the first, second, and third quartiles for the data below.

66, 67, 69, 69, 73, 74, 75, 75, 78, 79, 79, 79, 81, 81, 82, 83, 83, 86, 89, 92

16. Find the percentage of the standard normal distribution that lies in the following intervals.

a. between z = -0.87 and z = 1.44 b. greater than z =2.12 17. The chickens at a certain farm have a mean weight of 5.8 pounds with a standard deviation of 0.4 pound. The

weights of the chickens are closely approximated by a normal curve. What percentage of chickens weigh less than 6.1 pounds?

18. Pat and Chris both took a spatial abilities test (mean = 80, std. dev. = 8). Pat scores a 82 and Chris scored a 94.

Assuming that the scores are normally distributed, what percent of individuals would score between Pat and Chris?

19. Determine the amount of tip and the total bill for a ticket of $125.50 with a 30% tip.

20. A retail store has a winter coat that costs $60 and sells for $115. Find the percent markup.

21. An outdoor equipment store is selling a lawn tractor for $1095, which is 15% below cost. Find the original cost of the lawn tractor.

22. Find the interest earned on a deposit of $3,000 that is in a bank for 5 years 3 months earning simple interest at a rate of 4 ½ %.

23. Find the future value of $1000 deposited at 3.4% simple interest for 9 months.

24. Find the interest earned on an account that earns 2 ½ % interest compounded monthly over 5 years on a deposit of $5000.

25. Find the average daily balance, the finance charge, and next billing cycle’s balance for the following credit card

account if the billing period is May 9 through June 8, the previous balance was $700.00, and the annual interest rate is 22%.

May 17 payment $200 May 30 dinner $45.00 June 3 theater tickets $64.00

26. Roger recently started a new job as an actuary. He is married and has an annual salary of $195,000. Find his

monthly take-home pay after taxes.

27. When Ann was born, her parents deposited $10,000 into a special account for Ann’s college education. The

account earned 5% interest compounded monthly. How much will be in the account when Ann is eighteen? 28. Jim wants an IRA that will be worth $500,000 when he retires at 70. Determine how much he needs to deposit

at age 30 at 6 1

4 % compounded quarterly.