MATH 166 Exam II Sample Questions Use the histogram below to answer Questions 1-2: (NOTE: All heights are multiples of.05) 1. What is P (X 1)? (a) 0.00525 (b) 0.0525 (c) 0.4 (d) 0.5 (e) 0.6 2. What is E(X)? (a) 0.7 (b) 0.9 (c) 1.5 (d) 2.0 (e) 3.0 3. Old-time license plates consist of two letters followed by three digits. How many different license plates are there in which the first letter is a vowel, the last digit is odd, and letters and digits are not allowed to repeat? (a) 1,080,000 (b) 6,300 (c) 56,250 (d) 58,500 (e) 151,200 (f) 45,000 4. In how many different ways can eight Pokemon line up if Pikachu and Dedenne must be together and Squirtle, Bulbasaur, and Charizard must be together? (a) 40,320 (b) 120 (c) 512 (d) 1,440 (e) 3,360
5. How many different arrangements of the word REVEILLE are possible? (a) 120 (b) 512 (c) 1,440 (d) 3,360 (e) 40,320 6. In planning next semester s schedule you have to choose one of three possible math courses, one of four HIST/POLS courses, two of four science courses, and one of six kinesiology courses (for relaxation). How many different curricula are available for consideration? Ignore times, rooms, instructors, etc. (a) 432 (b) 864 (c) 6,188 (d) 10,296 (e) 103,680 7. A medical student knows 80 of the 100 diseases covered on the midterm. If 50 diseases are put on the exam, what is the probability that the student knows exactly 40 of them? (a) 1.066 10 6 (b) 1.917 10 11 (c) 0.1398 (d) 0.1969 (e) 0.8000 8. Which of the histograms below has the largest variance: 0.5 0.5 0.5 0.45 0.45 0.45 0.4 0.4 0.4 0.35 0.35 0.35 0.3 0.3 0.3 0.25 0.25 0.25 0.2 0.2 0.2 0.15 0.15 0.15 0.1 0.1 0.1 (I) -1 0.05 0-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 (a) I (b) II (c) III (d) I and III (e) all are equal (II) -1 0.05 0-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 (III) -1 0.05 0-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
9. A new drug is found to cause side effects in 35% of the people who take the drug. If 400 people take the drug, what is the mean and standard deviation (to two decimal places) of the number of people who will experience side effects? (a) µ = 140, σ = 91.00 (b) µ = 260, σ = 9.54 (c) µ = 140, σ = 11.83 (d) µ = 260, σ = 11.83 (e) µ = 140, σ = 9.54 10. An employer provides an annual insurance policy which covers against death and against disability. The policy pays $40,000 if the employee is disabled and $200,000 in the event of the employees death. The probabilities of these events happening in the next year are 0.002 and 0.0008, respectively. What is the minimum the employer should charge for this policy? (a) $160 (b) $240 (c) $432 (d) $857 (e) $1200 11. Given a bag of 75 M&Ms, 10 of which are green, consider the following random variables: Let X 1 be the number of M&Ms drawn from the bag, without replacement, until you get a green one. Let X 2 be the number of M&Ms drawn from the bag, with replacement, until you get a green one. Which statement below is true? (a) X 1 is finite discrete and X 2 is infinite discrete. (b) X 1 is infinite discrete and X 2 is finite discrete. (c) Both X 1 and X 2 are finite discrete. (d) Both X 1 and X 2 are infinite discrete. (e) None of these is true. 12. Eleven players of the US Women s National soccer team are to travel together to a charity dinner in a seven-seater SUV and a 4-seater sports car. How many different seating arrangements are possible if only Alex Morgan, Hope Solo, and Abby Wambach are willing to drive and the others don t care where they sit as long as they are not driving? (a) 2,177,280 (b) 1,088,640 (c) 483,840 (d) 6,652,800 (e) 39,916,800
13. A medical student creates 100 notecards about the diseases covered on the midterm. While studying, they draw a notecard at random, try to identify the disease, and replace the notecard in the pile, repeating this 50 times. If the student knows 80 of the diseases on the notecards, what is the probability that they will get exactly 40 correct? (a) 1.066 10 6 (b) 1.917 10 11 (c) 0.1398 (d) 0.1969 (e) 0.8000 14. The probability distribution of the number of chocolate chips in a cookie is shown below: x 4 5 6 7 8 P (X = x) 0.08 0.12 0.24 0.37 0.19 Find each of the following: (a) Mean: (b) Median: (c) Mode: (d) Variance: (e) Standard Deviation:
15. A fair coin is tossed 3 times. Let X = the number of heads. Find the probability distribution of X. 16. Suppose 85% of all Aggies are football fans. If you survey 100 Aggies... (a)...what is the probability that exactly 20 are NOT football fans? (b)...what is the probability that at least 75 are football fans? (c)...what is the probability that at least 71 but fewer than 86 are football fans?
17. The US Senate consists of 54 Republicans and 46 Democrats. (a) If a committee of 9 Senators is chosen at random, what is the probability that it contains exactly 5 Republican and 4 Democratic Senators? (b) If a committee of 9 Senators is chosen at random, what is the probability that it contains at least one Republican? 18. Five cards are drawn from a standard deck of 52 cards (a) If the cards are put back in the deck after each draw, in how many ways can at least one face card be drawn? (b) If the cards are not put back in the deck after each draw, in how many ways can exactly 1 king or exactly 2 queens be drawn?
19. Grade point averages of undergraduates at Texas A&M are normally distributed with a mean of 2.8 and a standard deviation of 0.4. (a) What is the probability that an A&M undergraduate selected has below a 2.5? (b) What is the probability that an A&M undergraduate selected has between a 2.0 and a 3.0? (c) Between what two grade point averages do the middle 45% of all undergraduates at Texas A&M have (to 2 decimal places)? 20. A carnival offers a game where the player pays $2 and then selects two marbles from a bucket containing 52 marbles, 4 of which are green. If the player draws two green marbles, they win $100. If they draw one green marble, they win $10. Otherwise, they win nothing. Let X =the player s net winnings. Find the probability distribution of X. 21. Scientists estimate that 57% of all men in their 40s have noticeable hair loss. If 300 men are selected at random, what is the probability that at least 100 but fewer than 130 do NOT have noticeable hair loss?