MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 MATH PRACTICE EXAM 3 Millersville University, Fall 008 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given question, determine whether an Euler circuit, a Hamilton circuit, or neither would solve the problem. ) The vertices of a graph represent food vendors at a local International festival and the edges ) represent paths between the food stands. A visitor wants to visit each food stand exactly once, returning to his starting point when he is done. A) Euler B) Neither Hamilton Solve. ) Determine how many Hamilton circuits a complete graph with 7 vertices has. A) 7 B) 7 6! D) 7! ) For the graph below, use the nearest neighbor algorithm to find an approximate minimum Hamilton circuit and its weight, starting at the indicated vertex. 3) 3) Starting at A A) A B C D E A; weight = B) A E B C D A; weight = 8 A C E B D A; weight = 9 D) A D B C E A; weight = 7 ) Sarah Katerinov is a high school student in Chicago. She will be going to college next year and is planning to visit the following campuses: University of Wisconsin at Madison, Harvard, and Ohio State University. How many different ways can she visit each of these schools and return to her starting point in Chicago? A) B) D) 6 ) Determine whether the graph has a Hamilton circuit. ) ) A) Yes B) No

2 Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, list and count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office. 6) Three representatives, if two must be male and one must be female 6) A) ACB, ACD, AEB, AED, CEB, CED, DEC, BEC, DEA, BEA, DCA, BCA; B) ACB, ACD, AEB, AED, CEB, CED; 6 ABC, CDE; D) ACB, ACD, AEB, AED; 7) At a lumber company, shelves are sold in 3 types of wood, 3 different widths and different lengths. How many different types of shelves could be ordered? A) B) 7 30 D) 7) 8) A baseball manager has 0 players of the same ability. How many 9 player starting lineups can he create? A) 90 B) 0 3,68,800 D) 36,880 8) 9) Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if there are no restrictions on the seating arrangement? A) 6,777,6 B) 0, D) 8 9) 0) How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members? Assume that no member can hold more than one office. A) 6 B) 36 D) 30 0) ) There are 3 members on a board of directors. If they must form a subcommittee of members, how many different subcommittees are possible? A) 7 B) 8,6 D) 7,60 ) ) Of the,98,960 different five-card hands possible from a deck of playing cards, how many would contain all black cards. A) 3,890 hands B) 3,60 hands 6,780 hands D) 63,0 hands ) If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? 3) The red die shows a 3. A) 6 ways B) way 3 ways D) ways 3) ) If a single card is drawn from a standard -card deck, in how many ways could it be an ace or a spade? A) 6 ways B) 7 ways way D) ways ) ) If you toss four fair coins, in how many ways can you obtain at least one head? A) 6 ways B) ways ways D) ways )

3 Find the probability. 6) A bag contains 9 red marbles, 8 blue marbles, and 6 green marbles. What is the probability that a randomly selected marble is blue? A) 9 3 B) D) 6 3 6) 7) 7) What are the odds in favor of spinning an A on this spinner? A) 6: B) :6 3: D) : 8) The table shows the number of college students who prefer a given pizza topping. 8) toppings freshman sophomore junior senior cheese meat veggie Find the empirical probability that a randomly selected student prefers cheese toppings. A) B) D) ) Mendel found no dominance in snapdragons with respect to red and white flower color. When pure red (RR) and pure white (rr) parents are crossed, the resulting Rr combination (one of each gene) produces second generation offspring with pink flowers. Suppose one of these second generation pinks is crossed with a pure white. What is the probability that the resulting snapdragon will have white flowers? A) 0. B) D) 0. 9) Find the probability of the following card hands from a -card deck. In poker, aces are either high or low. A bridge hand is made up of 3 cards. 0) In poker, a royal flush ( highest cards of a single suit) 0) A) B) D) Find the indicated probability. ) A bag contains red marbles, blue marbles, and green marble. If a marble is selected at random, what is the probability that it is not blue? ) A) 3 B) 6 D) 3 Find the probability. ) If you are dealt two cards successively (with replacement of the first) from a standard -card deck, find the probability of getting a heart on the first card and a diamond on the second. A) 3 0 B) 6 0 D) 69 ) 3

4 Use the general multiplication rule to find the indicated probability. 3) You are dealt two cards successively (without replacement) from a shuffled deck of playing cards. Find the probability that both cards are black. A) 6 B) 3 0 D) 3) Find the conditional probability. ) If a single fair die is rolled, find the probability that the number rolled is given that it is odd. ) A) 6 B) 3 D) 3 Find the indicated probability. ) An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer. A) 0 B) D) 0 ) Find the probability. 6) What is the probability that 3 rolls of a fair die will show three sixes? A) 0.08 B) D) ) 7) In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability that, from a random sample of 0 physics majors, no more than 6 belong to an ethnic minority. A) B) D) ) 8) Suppose a charitable organization decides to raise money by raffling a trip worth $00. If 3,000 tickets are sold at $.00 each, find the expected net winnings for a person who buys ticket. A) -$0.8 B) -$.00 -$0.8 D) -$0.83 8) Find the expected value of the random variable. 9) The random variable X is the number of houses sold by a realtor in a single month at the Sendsomʹs Real Estate office. Its probability distribution is given in the table. x P(X = x) A) 3.0 B) D) 3.0 9)

5 Use the given data to construct a frequency and relative frequency distribution. 30) A car insurance company conducted a survey to find out how many car accidents people had been involved in. They selected a sample of 3 adults between the ages of 30 and 70 and asked each person how many accidents they had been involved in in the past ten years. The following data were obtained. 30) Construct a frequency and relative frequency distribution using classes based on a single value. A) B) 0 0 0/3 3% 0 /00 = % /3 3% 0 0/00 = 0% /3 6% /00 = % 3 3 3/3 9% 3 3 3/00 = 3% /3 6% /3 3% 0 /3 3% 0 0/3 3% 6 6/3 9% 3 3 3/3 9% /3 3% /3 3% D) /00 = % /00 = % 0 /3 3% 0 0/3 3% /3 6% 3 3 3/3 9% /3 6% /3 3% Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 3) The five sales people at Southwest Appliances earned commissions last year of $,000, $,000, 3) $7,000, $8,000, and $3,000. Find the mean commission. A) $7,00 B) $8,60 $,80 D) $9,90 Find the mode or modes. 3), 9, 7, 3,, 8, 86,,, 6 A) 0. B) 9 8 D) No mode 3) Find the median for the given sample data. 33) The salaries of ten randomly selected doctors are shown below. 33) $,000 $7,000 $6,000 $0,000 $9,000 $7,000 $38,000 $7,000 $9,000 $93,000 Find the median salary. A) $7,000 B) $3,000 $6,000 D) $78,00

6 Find the range for the set of data given. 3) A) B) 6 D) 3) Find the standard deviation. Round to one more place than the data. 3) 9,, 7, 6,,,, 6, A). B)..7 D).7 3) 6

7 Answer Key Testname: MATH 00 PRACTICE TEST3 FALL 08 ) C ) C 3) B ) D ) B 6) B 7) D 8) C 9) B 0) D ) A ) C 3) A ) A ) D 6) B 7) C 8) A 9) D 0) A ) A ) B 3) C ) C ) C 6) C 7) B 8) D 9) C 30) D 3) A 3) D 33) D 3) A 3) D 7