Math 1332 Review Test 4 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem by applying the Fundamental Counting Principle with two groups of items. 1) In how many ways can a girl choose a two-piece outfit from 7 blouses and 6 skirts? 2) How many different four-letter secret codes can be formed if the first letter must be an S or a T? 3) You are taking a multiple-choice test that has 7 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions? Use the Fundamental Counting Principle to solve the problem. 4) You want to arrange 9 of your favorite CD's along a shelf. How many different ways can you arrange the CD's assuming that the order of the CD's makes a difference to you? Evaluate the factorial expression. 5) 9! 7! Use the formula for n P r to evaluate the expression. 6) 9 P 4 7) In how many distinct ways can the letters in ACCOUNTING be arranged? In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 8) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded? Use the formula for n C r to evaluate the expression. 9) 14 C 8 10) From 8 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? 11) In how many ways can a committee of three men and four women be formed from a group of 10 men and 10 women? Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 12) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 7. 1
13) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 7. 14) A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss. 15) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 10. 16) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 3 or 4. Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary. 17) In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily? How frequently? Response Daily 236 Weekly 284 Monthly 277 Couple times a year 137 Don't track 57 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 18) Christine, Michael, Hunter, Keren, Angela, and Antonio have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Hunter arrive first and Angela last? Find the probability that Hunter will arrive first and Angela will arrive last. A) 720; 15; 1 48 B) 120; 10; 1 12 C)120; 6; 1 20 D) 720; 24; 1 30 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 19) If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards are picture cards. (There are 12 picture cards.) 20) A committee consisting of 6 people is to be selected from eight parents and four teachers. Find the probability of selecting three parents and three teachers. 2
21) A random sample of 30 high school students is selected. Each student is asked how much time he or she spent watching television during the previous week. The following times (in hours) are obtained: 6, 14, 8, 11, 8, 6, 8, 7, 5, 11, 9, 7, 7, 6, 9, 8, 5, 5, 10, 7, 5, 7, 14, 9, 6, 10, 6, 9, 8, 7 Construct a frequency distribution for the data. 22) A random sample of 30 attorneys is selected. The following list gives their ages: 30, 58, 42, 45, 55, 63, 52, 41, 29, 35, 43, 31, 61, 44, 60, 32, 29, 39, 44, 51, 38, 31, 48, 53, 67, 54, 30, 53, 72, 71 Construct a stem-and-leaf plot for the data. What does the shape of the display reveal about the ages of the attorneys? 23) Six people from different occupations were interviewed for a survey, and their annual salaries were as follows: $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the mean annual salary for the six people? Find the median for the group of data items. 24) 97, 97, 91, 47, 72, 97 Find the mode for the group of data items.if there is no mode, so state. 25) 1.3, 2.3, 1.5, 2.9, 1.3, 2.3, 1.3, 8.1, 8.1, 1.9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange. 26) A company advertised that, on the average, 95% of their customers reported "very high satisfaction" with their services. The actual percentages reported in 15 samples were the following: 95, 95, 92, 57, 71, 95, 92, 71, 95, 95, 57, 92, 92, 95, 57 a. Find the mean, median, mode and midrange. b. Which measure of central tendency was given in the advertisement? c. Which measure of central tendency is the best indicator of the "average" in this situation? A) a. mean = 83.4, median = 92, mode = 95, midrange = 76 c. mode B) a. mean = 83.4, median = 92, mode = 95, midrange = 76 c. mean C)a. mean = 83.4, median = 92, mode = 95, midrange = 76 b. median c. mean D) a. mean = 83.4, median = 92, mode = 95, midrange = 76 c. median 3
Answer Key Testname: MATH 1332 T4RF15 1) 42 2) 35,152 3) 78,125 4) 362,880 5) 72 6) 3024 7) 907,200 8) Permutations, because the order of the prizes awarded matters. 9) 3003 10) 56 11) 25,200 12) 0 13) 2 13 14) 1 2 15) 1 12 16) 2 5 17) 236 991 ; 0.238 18) D 33 19) 108290 20) 8 33 21) Hours Number of of TV HS Students 5 4 6 5 7 6 8 5 9 4 10 2 11 2 14 2 22) Stems Attorneys 2 99 3 00112589 4 1234458 5 1233458 6 0137 7 12 The ages tend to be concentrated in the middle of the range. 4
Answer Key Testname: MATH 1332 T4RF15 23) $47,750 24) 94 25) 1.3 26) B 5