Math 1342 Practice Test 2 Ch 4 & 5 Name 1) Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. 1) List the outcomes of the sample space. 2) If two dice are rolled one time, find the probability of getting a sum of 6. 2) 3) Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using the figure below, how many outcomes are possible if both numbers are even? 3) 4) There are 27,842 undergraduate students enrolled at a certain university. The age distribution is as follows: 4) Age Range Number 13-14 2 15-17 49 18-22 11,563 23-30 9568 31 and up 6660 Total 27,842 What is the probability that a student is between 23 and 30 years old? 1
5) A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. 5) The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Greater than 4). 6) A single card is drawn from a deck. Find the probability of selecting a heart or a 8. 6) 7) An apartment building has the following distribution of apartments: 7) 1 bedroom 2 bedroom 3 bedroom 1st floor 3 1 1 2nd floor 1 3 2 3rd floor 1 4 1 If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms? 8) If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade? 9) On a certain day, a cheese packaging facility packaged 490 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. 8) 9) Minor Flaw No Minor Flaw Major Flaw 16 36 No Major Flaw 63 375 Find the probability that randomly chosen cheese package has a major flaw. 10) Let A and B be events with P(A) = 0.7, P(B) = 0.3, and P(B A) = 0.2. Find P(A and B). 11) Let A, B and C be independent events with P(A) = 0.1, P(B) = 0.7, and P(C) = 0.9. Find P(A and B and C). 12) A fair coin is tossed four times. What is the probability that the sequence of tosses is HHHT? 10) 11) 12) 2
13) Below are listed the numbers of engineers in various fields by sex. Choose one engineer at random. Find P(electrical male). Mechanical Electrical Biomedical Male 9691 4997 6064 Female 2061 1015 5937 13) 14) Evaluate the permutation: 10 P 8 14) 15) Evaluate the combination: 12 C 8 15) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 16) The number of different arrangements of four pictures from a selection of ten pictures is 5,040. A) False B) True 16) 17) There are 3 different mathematics courses, 3 different science courses, and 5 different history courses. If a student must take one of each, how many different ways can this be done? 18) On a TV game show, a contestant is shown 8 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen items need not be in any particular order. In how many ways can the contestant choose the three items? 19) A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is 20) A committee consist of 8 women and 11 men. Three members are chosen as officers. What is the probability that all three officers are women? 21) Determine whether the table represents a discrete probability distribution. 17) 18) 19) 20) 21) x P(x) 1 0.45 2 0.2 3 0.4 4-0.05 3
22) Fill in the missing value so that the following table represents a probability distribution. 22) x -4-3 -2-1 P(x) 0.42 0.08? 0.05 23) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find P(1 or more). 23) x 0 1 2 3 4 P(x) 0.05 0.69 0.16 0.08 0.02 24) A survey asked 851 people how many times per week they dine out at a restaurant. The results are presented in the following table. 24) Number of Times Frequency 0 104 1 244 2 242 3 142 4 62 5 22 6 27 7 8 Total 851 Consider the 851 people to be a population. Let X be the number of times per week a person dines out for a person sampled at random from this population. Find the probability that a person does not dine out at all. 25) For the following data, construct a graph showing the probability distribution. X 0 1 2 3 4 P(X) 0.35 0.25 0.20 0.15 0.05 25) 26) Construct the probability distribution for the number of heads obtained when tossing four coins. Draw a graph of the distribution. 26) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) Continuous random variables are obtained from data that can be measured rather than counted. A) True B) False 27) 4
28) Determine whether the random variable described is discrete or continuous. The total value of a set of coins 29) Determine whether the table represents a discrete probability distribution. 28) 29) x P(x) 5 0.45 6 0.45 7 0.15 8-0.05 30) If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game? 31) The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. 30) 31) Number of cartoons watched X 0 1 2 3 4 5 Probability P(X) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. 32) The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. 32) Number of cartoons watched X 0 1 2 3 4 5 Probability P(X) 0.15 0.20 0.30 0.10 0.20 0.05 What is the mean of the data? 33) Compute the mean of the random variable with the given discrete probability distribution. 33) x P(x) 0 0.45 15 0.05 20 0.5 30 0 5
34) Compute the probability of X successes. n = 5, X = 4, p = 0.7 34) 35) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 11, p = 0.7, P(9) 35) 36) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n =12, p = 0.7, P(3 or fewer) 36) 37) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 19 adult dogs is studied. What is the mean number of dogs who weigh 65 lb or more? 37) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 38) Using the probability distribution listed, the mean would be 1.6. 38) X 0 1 2 3 P(X) 0.2 0.1 0.3 0.4 A) False B) True 39) A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers. 39) 40) A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen, what is the probability that there will be 2 white marbles and 6 black marbles? 40) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 41) The probability that a Poisson random variable X is equal to 4, where = 7, is 41) A) 11! 7!4! B) e-4 4 7 7! C) e-7 7 4 4! D) 7!4! 11! 42) Give the variance of the following distribution? 42) X 0 1 2 3 4 P(X) 0.20 0.35 0.10 0.25 0.10 6
Answer Key Testname: MATH 1342 PRAC TEST 2 FL_18_SA 1) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 5 2) 36 3) 4 4) 0.344 5) 2/3 4 6) 13 7) 11 17 8) 17 52 9) 0.106 10) 0.14 11) 0.063 12) 0.0625 13) 0.241 14) 1,814,400 15) 495 16) B 17) 45 18) 56 1 19) 21 20) 0.0578 21) No 22) 0.45 23) 0.95 24) 0.122 7
Answer Key Testname: MATH 1342 PRAC TEST 2 FL_18_SA 25) 26) Number of Heads X 0 1 2 3 4 1 1 3 1 1 Probability P(X) 16 4 8 4 16 27) A 28) discrete 29) No 30) $3.06 31) 1.46 32) 2.15 33) 10.75 8
Answer Key Testname: MATH 1342 PRAC TEST 2 FL_18_SA 34) 0.360 35) 0.1998 36) 0.0017 37) 8.55 38) A 39) Mean = 6.7, Variance = 2.2 40) 30 C 2 30 C 6 60 C 8 41) C 42) 1.71 9