7. If 3/5 of the students at a school are women, what is the probability that in a group of 30 students, there are at most 18 men?

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1 MATH 1333 Final Exam Review 1. One-hundred-fifty people were asked what they put in their coffee. 54 said they used cream, 72 said they used sugar. 62 said they did not use cream or sugar. What is the probability a person selected from this group used cream and sugar? 2. Tom has 3 different CDs of Elvis, 2 different CDs of the Black Eyed Peas and 4 different CDs of Aerosmith. In how many ways can those CDs be placed on a shelf so that CDs by the same group are next to each other. 3. Using the histogram to the right determine how high the bar above the 5 should be drawn and answer the five questions below. (a) What is the mode? (b) What is the standard deviation? (c) What is the median? (d) What is the variance? (e) What is the mean? 4. Two fair six-sided dice are cast (one green and one red). What is the probability the red die rolled an even number, if it is known that the sum of the two dice was greater than 8? 5. The highway department has found that only 62% of all drivers carry valid insurance information with them. If 30 cars are stopped for a routine insurance check, what is the probability that at least 18 of them have valid insurance with them? 6. In the 2008 presidential election, over 130 million people voted, of which 46.3% were male. Of the male voters, 49% voted for Obama and 48% voted for McCain. Of the female voters, 56% voted for Obama and 43% voted for McCain. Source: U.S. Census and The New York Times (a) Find the probability that a randomly selected voter is a male, given that he voted for McCain. (b) Find the probability that a randomly selected voter did not vote for McCain or Obama. 7. If 3/5 of the students at a school are women, what is the probability that in a group of 30 students, there are at most 18 men? 8. In a survey asked of 75 students this morning, 59 said they ate breakfast, 48 said they ate breakfast AND read the Battalion, and 7 said they didn t do either of these things. How many of the students surveyed read the Battalion? 9. On a given class day, 18% of students are not listening in class. If 25 students are chosen at random, what is the probability at most 15 of them are listening? 10. Based on the numbers given about the stuffed animals in the table, if a teddy bear is randomly chosen, what is the probability that it is brown? teddy bear monkey puppy dog brown black 3 4 2

2 Math 1333 Final Exam Review page Box A has 2 green and 5 blue marbles in it. Box B has 9 green and 6 blue marbles in it. A marble is drawn from Box A, transferred to Box B, and then a marble is drawn from Box B. What is the probability a blue marble was drawn from Box A, if you know a green marble was drawn from Box B? 12. The average GPA for the graduating class at Bryan High School this year was a 1.96 with a standard deviation of If the GPA's are normally distributed, what is the lowest GPA a student in the graduating class could have and still be in the top 25% of the class? 13. A local high school math teacher conducted a survey to find out the correlation between students who were suspended from school and whether or not they passed their math class. How many girls were suspended and failed? NOTE: Two of the numbers in the Venn diagram have been filled in for you. 51 boys were surveyed 10 boys who got suspended still passed 42 students failed 48 girls did not get suspended 30 boys passed the class 17 boys were suspended and failed 14. Four boys and five girls are randomly assigned seats in a row. What is the probability that all the girls sit together and all the boys sit together? 15. Cheryl has a cooler with 4 Dr. Peppers and 7 Cokes inside. If 2 drinks are randomly drawn out, in succession, without replacement, what is the probability that the two drinks are the same brand? 16. It has been found that the amount of money customers spend at Freebirds can be normally distributed. Customers spend an average of $7.15 with a standard deviation of $0.75. Tanner is going to Freebirds tonight. What is the probability he will spend more than $8? 17. A recent study found that 83% of college freshman were involved in volunteer work at least occasionally. Suppose a random sample of 12 college students is taken. Find the probability exactly 7 did not volunteer occasionally. 18. Let n( U) = 26, n( A B) = 6, n( A) = 14, and n( B) = 11. Find ( ) n A. 19. The probability that Dr. Poage will give a quiz on any given day is If we have 18 class days left, what is the probability she gives exactly seven more quizzes? 20. A bag contains bean-bags: 3 black bags, 1 blue bag, 6 red bags, and 9 green bags. A game consists of randomly pulling out 2 bean-bags at the same time. If you pull out two of the same color, you win $4. If you pull out the blue, you win $6. For everything else, you lose your money. It costs $1.50 to play the game. Let the random variable X denote the net winnings. (a) Find the probability distribution associated with this experiment. (b) Find the expected value of X and explain your answer.

3 Math 1333 Final Exam Review page Certain codes are formed with 2 letters, followed by 3 digits, followed by 2 more letters (no spaces). If the first letter must be a vowel, the first digit must be odd, and no letter or digit can be repeated, how many different codes are possible? 22. At a party some of the guests brought cookies, drinks, or candy. How many total guests were at the party? 5 guests brought cookies, candy and drinks 19 guests brought exactly 2 items 21 guests brought drinks 20 guests did not bring cookies 8 guests brought only candy 2 guests did not bring a drink or candy 5 guests brought only cookies and drinks 11 guests brought drinks and candy 23. A classroom of people were asked how many speeding tickets they had received during their lifetime. Let the random variable, X, denote the number of speeding tickets. Based upon these results, answer the following 4 questions. number of people number of speeding tickets (a) How many tickets would you expect somebody from this classroom to have? (b) What is the median for the number of tickets these people had received? (c) What is the probability a person in the class had received more than 2 tickets? (d) What is the standard deviation in the number of tickets received? 24. A box of t-shirts has 7 small, 3 medium, 5 large, and 4 X-large t-shirts inside. Eric pulls out t-shirts 1 at a time until he has 2 small. Let the random variable, X, denote the number of shirts he pulls out of the box. What values may X assume? A C B 25. Shade a Venn diagram representing: ( ) 26. A survey was conducted of 475 students living in dorms at Texas A&M. There were 327 students who had a refrigerator in their dorm room, 186 had a microwave in their dorm room, and 30 did not have a refrigerator nor a microwave in their dorm room. What is the probability a student selected at random had BOTH a refrigerator and a microwave in their dorm room? 27. In a certain area, 18% of the population are joggers and 45% of the joggers are women. If 60% of those who do not jog are women, find the probability that a person selected at random from this community is a jogger given that the person is a man? 28. A band has 9 officers consisting of a Drum Major, an Assistant Drum Major, a Band Sweetheart, and 6 Council Members. There are 193 boys among the 354 band members. If the Drum Major must be a boy and the Band Sweetheart must be a girl, in how many different ways could these officers be selected. (SHOW ALL WORK!)

4 Math 1333 Final Exam Review page The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. What is the probability that an individual s clotting time will be less than 3 seconds or greater than 13 seconds? Assume normal distribution. 30. Which of the following sets best describes the shaded part of the Venn diagram? (b) ( C A) B (c) ( ) (a) ( B C) A (d) ( A C) B (e) none of these A B C 31. The average resident of Oxnard, CA spends 42 minutes per day commuting, with a standard deviation of 12 minutes. Assume a normal distribution. Find the percent of all residents in Oxnard who commute between 38 and 60 minutes per day. 32. Mrs. Tate is selecting a group of students to help her grade the exams. She needs a coordinator, a grade recorder, 3 graders for the multiple choice, and 5 graders for the work-out problems. The coordinator and grade recorder must be selected from 7 graduate students. The graders must be selected from 13 undergraduate students. (NOTE: Each student can only hold one position and graders cannot grade both multiple choice and work-out problems.) In how many ways can Mrs. Tate select her helpers? 33. If n( U) = 33, n( A B) = 29, n( A B) = 5, and n( B ) = 23, find ( ) n A. 34. Shelbi flips a weighted coin 120 times. The probability it lands on tails is What is the probability the coin lands on HEADS at least 40 times? 35. A group consists of 3 boys and 6 girls. They are all arranged randomly in a row. What is the probability a girl is at each end and a girl is in the middle seat? 36. A survey of 150 A&M students were asked which football activities they attended last weekend. Use the Venn diagram below to help figure out how many students ONLY went to the game. (note: 2 numbers have been filled in for you) 73 tailgated 22 went to midnight yell, tailgated, and attended the football game 48 did not attend the football game 30 went to midnight yell and the game 47 tailgated, but did not go to midnight yell How many students ONLY went to the game? 37. Assume that p is true and that q and r are both false. Indicate whether the compound statements below are true or false: a) ~ p ~ r b) p (q ~ r)

5 38. Construct a truth table for the statements below. Also, state whether each one is a tautology, contradiction, or neither. a) ~ (q ~ p)) b) (p (q ~ r)) ~ q 39. Let p and q be any statements. Construct a truth table for: ( ~(p q ) q) ~p p q T T T F F T F F 40. Use a truth table to determine if these statements are equivalent: p ( q r) and ~ p ( q r). 41. Draw the circuit represented by the symbolic statement ~ p ( q r) Math 1333 Final Exam Review page Write a symbolic statement that represents the circuit shown. 43. Consider the frequency table below for the random variable X. X Frequency Find the: a) mean b) median c) mode d) standard deviation e) variance 44. The table below shows the number of Mad about Math magazine subscribers (in millions) on December 31 st of the given years. Year Subscribers a) Find the linear equation of best fit (the least-squares regression line) for this data. Express the number of subscribers (in millions) as a function of the number of years since Round the slope and y-intercept of the line to 3 decimal places. b) If the trend continues, estimate the number of subscribers the magazine will have on June 30 th of c) When would you expect the number of magazine subscribers to reach 12,000,000?