MDM4U - Sample Mastery - mrblakely

MDM4U - Sample Mastery Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. A set of data has a range of 160. A histogram displaying the data has 8 bars. What is the bin width? a. 8 c. 152 b. 20 d. 168

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2. A histogram has a bin width of 0.5. The left end point of the first interval is 7.25. What is the left end point of the sixth interval? a. 9.75 c. 12.25 b. 10.25 d. 13.25

____

3. Rolling a die a large number of times and recording the number on the top face should result in a distribution that is a. U-shaped c. mound-shaped b. uniform d. skewed

____

4. A mound-shaped distribution is symmetrical about a vertical line passing through a. the origin c. the interval with greatest frequency b. the interval with smallest frequency d. none of the above

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5. The senior soccer team includes students from all grades but most of its members are from the higher grades. The distribution of the ages of team members would likely be a. U-shaped c. right-skewed b. mound-shaped d. left-skewed

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6. What are the mean and median (in that order) for the set {2, 5, 2, 8, 3}? a. 2, 4 c. 4, 2 b. 3, 4 d. 4, 3

____

7. Find the median and mode (in that order) for the concert ticket prices (in dollars): 35, 55, 38, 35, 37 a. 37, 35 c. 37, 40 b. 28, 35 d. 38, 40

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8. A set of data has the following proporties: mean = 17, median = 15, mode = 14. Which of the following best descibes the data set? a. skewed left c. skewed but neither left nor right b. skewed right d. not skewed

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9. What is the mean mass (in grams) of the screws with masses as tabulated below? Mass (g) Frequency a. 8.0 b. 8.25

7.0 1

7.5 2

8.0 7

8.5 4

9.0 6

c. 8.3 d. 8.5

____ 10. Find the mean engine displacement (in cubic centimetres) for the cars in a parking lot.

Displacement (cm3) Frequency

1000–2000 8

2000–3000 10

a. 2000 b. 2040

3000–4000 5

4000–5000 2

c. 2500 d. 2540

____ 11. What is the modal interval for the sprint times (in seconds) tabulated below? Time (s) Frequency

9.80–9.89 2

9.90–9.99 4

a. 9.80-9.89 b. 9.90-9.99

10.00–10.09 6

10.10–10.19 8

c. 10.00-10.09 d. 10.10-10.19

____ 12. On a fishing trip, Ella caught 6 bass with a mean mass of 1.5 kg and 4 pike with a mean mass of 3.5 kg. What was the mean mass, in kilograms, of all of the fish Ella caught? a. 1.5 c. 2.5 b. 2.3 d. 3.5 ____ 13. The mark in Diana’s statistics course is based on 60% for term work and 40% for the examination. What mark did she receive for her term work if her final mark was 76 and she received 70 on the exam? (All marks are out of 100.) a. 60 c. 80 b. 76 d. 82 ____ 14. The mean of a set of 5 numbers is 26. What would the mean be if one of the numbers was increased by 10? a. 10 c. 28 b. 26 d. 36 ____ 15. The mean of a set of 4 number is 19. What would the mean be if each of the numbers was decreased by 11? a. 8 c. 19 b. 11 d. 30 ____ 16. The median age in years, of six students, all of whose ages are different, is 17. What would the median be if the third youngest student was one year older? a. 16 c. 17 b. 16.5 d. 17.5 ____ 17. Find the range of the following set of data: 3, 4, 0, 5, 2, 8 a. 4 c. 8 b. 5 d. 12 ____ 18. Calculate the standard deviation, to the nearest whole number, of the numbers of words in each of these student essays: 700, 740, 810, 900, 1000 a. 109 c. 300 b. 230 d. 11 840 ____ 19. State the standard deviation of the numbers of taxi passengers to the nearest decimal place. Number of Passengers Frequency a. 0.8

1 24

2 14

3 10 c. 1.0

4 2

b. 0.9

d. 1.1

____ 20. How many of the numbers in the set below are within two standard deviations of the mean? 0, 2, 4, 6, 7, 8 a. 3 c. 6 b. 4 d. 8 ____ 21. If each number in a set is increased by two, which of the following measures of spread would remain unchanged? a. the range c. the standard deviation b. the IQR d. all the above ____ 22. If X~N(15, 22), then 68% of the data fall in the interval a. 9–21 c. 13–17 b. 11–19 d. 15–17 ____ 23. If X~N a. 34% b. 47.5%

, what percent of the data fall between and c. 50% d. 95%

?

____ 24. IQ is normally distributed with a mean of 100 and a standard deviation of 15. What percent of the population has an IQ less than 55? a. 0% c. 0.3% b. 0.15% d. 5% ____ 25. The masses of 500 boxes of sugar are approximately normally distributed with a mean of 150g and a standard deviation of 3g. How many of these boxes would you expect to have a mass greater than 150g? a. 250 c. 256 b. 253 d. 259 ____ 26. The nicotine content in a certain brand of cigarettes has a normal distribution with a mean of 1.5 mg and a standard deviation of 0.2 mg. What percent of these cigarettes have a nicotine content less than 0.7 mg? a. 5% c. 0.15% b. 0.3% d. less than 0.15% ____ 27. Suppose that masses of newborn children are normally distributed with a mean of 3.4 kg and a standard deviation of 0.8 kg. A newborn is potentially at risk if the baby’s mass falls in the lowest 2.5%. These babies have a mass less than a. 3.4 kg c. 1.8 kg b. 2.6 kg d. 1.0 kg ____ 28. The variable has a normal distribution with 99.7% of the area under its curve falling symmetrically between x = 50 and x = 170. Its mean and standard deviation are respectively a. 110 and 20 c. 120 and 20 b. 110 and 202 d. 120 and 202 ____ 29. Diameters of ball bearings produced in a certain plant have a mean of 24.50 mm and a standard deviation of 0.15 mm. In what interval will the diameters of acceptable ball bearings fall if the manufacturer rejects the smallest 2.5% and largest 0.15%? (Assume a normal distribution) a. 24.05–24.80 c. 24.20–24.80 b. 24.05–24.95 d. 24.20–24.95 ____ 30. The z-score corresponding to the 44th percentile is

a. b.

2.62 0.15

c. 0.44 d. 4.40

____ 31. Given a normally-distributed data set whose mean is 40 and whose standard deviation is 8, what value of x would have a z-score of 1.25? a. 10 c. 30 b. 10 d. 50 ____ 32. The volume of cola in 355-mL cans is normally distributed with a standard deviation of 3 mL. What percent of cans have a volume greater than 359 mL? a. 9.18% c. 64.1% b. 35.9% d. 90.82% ____ 33. To earn a scholarship, Luc needs to score in the top 8% on an entrance test. If test marks are normally distributed with a mean of 500 and a standard deviation of 38, what mark (to the nearest whole number) is he aiming for? a. 446 c. 553 b. 447 d. 554 ____ 34. Find the percentile corresponding to x = 15 if X~N(12, 2.62). a. 12th c. 87th b. 13th d. 86th ____ 35. The number of candies in a bag is normally distributed with a mean of 200 and a standard deviation of 3. In what percentile is a bag with 205 candies? a. 2nd c. 71st b. 70th d. 95th ____ 36. The masses of bolts made in a plant are normally distributed. Bolts will be rejected if their z-scores are greater than 2.15 or less than 2.10. What percent of bolts will be rejected? a. 0% c. 1.79% b. 1.58% d. 3.37% ____ 37. The diameters of inflated balloons, in millimetres, are normally distributed with a mean of 200 and a standard deviation of 12. Balloons will burst if their diameters exceed 210. What percent of balloons will burst? a. 16.67% c. 79.67% b. 20.33% d. 83.37% ____ 38. How many people in a group of 60 will have an IQ less than 92 if their IQs are normally distributed with a mean of 100 and a standard deviation of 15? a. 18 c. 30 b. 29 d. 42 ____ 39. The diameters of the lead in 1500, 0.7-mm mechanical pencils are normally distributed with a standard deviation of 0.02. How many of these pencils will have lead diameters greater than 0.75? a. 2.5 c. 99 b. 9 d. 1491 ____ 40. The heights, in centimetres, of the 700 female students in a high school are normally distributed with a mean of 158 and a standard deviation of 6. Approximately how many of these students have a height between 151 cm and 165 cm? a. 528 c. 536 b. 534 d. 530

Short Answer 41. A histogram for a data set has a smallest value of 12 and a greatest value of 50. Its bin width is 8. What is the number of intervals in this histogram? 42. A histogram representing a skewed distribution has its greatest frequency on the left. In what direction is it skewed? 43. State the mean and median for the data set {2, 5, 7, 1, 3}. 44. Find the mean, median, and mode of the pop quiz marks shown below. Mark Frequency

0 1

1 1

2 3

3 5

4 8

5 2

45. In a certain course, a student’s final mark is computed using the following weights: Quizzes 10%, Tests 40%, and Examination 50%. Find Alfredo’s final mark if his marks, out of 100, in each of these categories 81, 75, and 70 respectively. 46. Find the mean age, to one decimal place, in years. Age (years) Frequency

6–10 2

11–15 4

16–20 7

21–25 1

47. The table below shows the average number of hamburgers consumed weekly by the students in Mr. Lee’s class. Find the median. Number of Hamburgers

0

1

2

3

4

5

6

7

Frequency

2

1

6

4

5

3

4

2

48. The table below lists the heights in centimetres of all of the teachers in a school. Find the modal interval. Height (cm) Frequency

150–159 6

160–169 10

170–179 20

180–189 18

190–199 4

49. The 18 students in Mr. Cho’s period 1 class had a mean final mark of 72.0%. The 22 students in his period 2 class had a mean final mark of 66.0%. Find the combined mean final mark of the two classes. 50. Find the range of the following data set: 2, 7, 0, 1, 5, 9 51. State the first and third quartiles for the bus stop waiting times in minutes: 10, 5, 7, 6, 7, 5, 4, 12 52. Find the standard deviation to one decimal place of the ages, in years, of these five siblings: 10, 12, 12, 17, 20 53. What is the interquartile range of the sizes of computer files (in kB) listed below?

Size (kB) Frequency

25 6

30 3

35 4

40 7

54. Find the standard deviation, to one decimal place, of the IQ scores listed below: IQ Frequency

80 3

90 4

100 8

110 3

120 2

55. The masses in grams of seven kittens in a litter are: 400, 450, 500, 500, 550, 650, 800. How many of the kittens have a mass within one standard deviation of the mean? 56. A set of numbers has Q2 = 22 and Q3 = 73. What would the values of these be if all of the numbers in the set were decreased by 7? 57. The interquartile range of salaries for executives in a large corporation is $150 000. What would the interquartile range be if each of the executives received a $50 000 raise? 58. X~N(12.2,

) and 99.7% of data fall within the interval 11.6–12.8. What is the standard deviation?

59. If X~N(105, 42), then what percent of the data are contained in the interval 97–105? 60. For X~N

, what percent of the data fall between

and

?

61. The time that a certain top sprinter takes to run the 100-m dash is normally distributed with a mean of 9.8 s and a standard deviation of 0.2 s. In what percent of his sprints will his time be less than 10.0 s? 62. An internet site has an average of 2500 hits per day. The number of daily hits is approximately normally distributed with a standard deviation of 220. For how many of the next 50 days would you expect the site to receive fewer than 2280 hits? 63. The numbers of books checked out daily at a local library are normally distributed with a mean of 240. Find the standard deviation if on 2.5% of the days there are fewer than 210 books checked out? 64. Find the variance if X~N(0,

) and 95% of the data are between 7 and 7.

65. Ravi’s math contest result put him in the 97th percentile. If 4000 students competed, how many had a score higher than Ravi’s score? 66. What percentile corresponds to a normal z-score of 1.24? 67. The numbers of peanuts in a bag are normally distributed with a mean of 150 and a standard deviation of 8. What percent of bags have fewer than 140 peanuts? 68. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What IQ (to the nearest whole number) is required to be in the top 15? 69. In X~N(12, 22), what percent of the data is between 10 and 13?

70. A box contains balls with the numbers 1 to 40 on it. One ball is drawn randomly. The probability of

the event :choosing a number divisible by 3 is to be determined. State the value of

.

71. What is the probability of rolling a sum greater than ten with two six-sided dice? 72. Two six-sided dice are rolled. Determine the probability of rolling pairs or a sum of four. 73. Statistics show that at a mini-putt course, 40% of customers are male. Of the male customers, 30% are smokers. Of the

female customers, 20% are smokers. If a customer is chosen at random, determine the probability that the customer is a male non-smoker.

74. Two six-sided dice are rolled. What is the probability that the total will be an odd number given that

a number less than four was rolled on the red die?

75. A card is drawn from a regular deck of cards and replaced. Then a second card is drawn. Determine

the probability that a spade is drawn and then a face card is drawn.

76. A bag contains 4 red marbles, 3 blue marbles, 6 black marbles, and 2 yellow marbles. If a marble is

drawn at random, determine the probability of drawing a red marble or a blue marble.

77. A spinner is divided into 21 equal sectors, numbered 1 through 21. Determine the probability of

spinning an even number.

78. A spinner is divided into 21 equal sectors, numbered 1 through 21. Determine the probability of

spinning a even number or a number divisible by 5.

79. Two six-sided dice are rolled. What is the probability of rolling a sum greater than 9? 80. The letters of the word SIMILE are scrambled. Determine the probability that the word is spelled exactly backwards 81. The letters of the word SIMILE are scrambled. Determine the probability that the word is spelled starting with S. 82. The letters of the word SIMILE are scrambled. Determine the probability that the word is spelled starting with The Two Is. 83. Determine the probability of choosing the Jack of Hearts and the King of Clubs out of a regular deck of 52 cards when two cards are randomly chosen without replacement. 84. Determine the probability of choosing the Ace of clubs and Jack of clubs out of a regular deck of 52 cards when two cards are randomly chosen withtout replacement. 85. The starting line up of a co-ed volleyball team must be made up of 3 males and 3 females. If the team has 10 females and 9 males to choose from, determine the probability that Emma, Mary, and Carolyn are selected for the line up.

86. A bag contains 2 green blocks, 4 purple blocks, and 6 red blocks. If four blocks are drawn one at a

time, without replacement, determine the probability that the order is red, red, purple, green.

87. Three cards are drawn from a regular deck, one at a time, without replacement. Determine the probability that the order is a jack, queen, and then a number 4, 5, or 6. 88. Nine Students enter a race. What is the probability that Joanna finishes last and Samantha finishes first? 89. Three die are rolled simultaneously. Determine the probability that a sum of 4 will be rolled. 90. A committee of 3 students is chosen from 6 music students and 5 drama students. Determine the probability that exactly 2 are drama students.

MDM4U - Sample Mastery Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

B A B C D D A B C D D B C C A D D A B C D C A B A D C A D B C A D C D D B A B D

SHORT ANSWER 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

The number of intervals in this histogram is 5. The distribution is skewed to the right. The mean is 3.6 and the median is 3. The mean = 3.2, the median = 3.5, and the mode = 4. Alfredo’s final mark is 73. The mean age, to one decimal place, is 15.5 years. The median number of hamburgers is 4. The modal interval is 170–179. The combined mean final mark of the two classes is 68.7%. The range is 10. The first quartile is 5 minutes and the third quartile is 8.5 minutes. The standard deviation is 3.7 years. The interquartile range of the sizes of computer files is 15 kB. The standard deviation is 11.5. There are 5 kittens that have a mass within one standard deviation of the mean. The value of Q2 would be 15 and the value of Q3 would be 66. The interquartile range would be $150 000. The standard deviation is 0.2. The percent of the data contained in the interval is 47.5%. The percent of the data that fall between and is 81.5%. Approximately 84% of his sprints will be less than 10.0 s. The site would receive fewer than 2280 hits on 8 of the next 50 days. The standard deviation is 15. The variance is 12.25. The number of students with a score higher than Ravi’s is 120. The percentile that corresponds to a z-score of 1.24 is the 89th percentile. The percent of bags that have fewer than 140 peanuts is 10.56%. An IQ of 116 is required to be in the top 15. The percent of the data between 10 and 13 is 53.28%. is 13

71. 72. 73. 0.28 74. 75. 76. 7/15 77. 10/21

78. 12/21=4/7 79. 1/6 80. 81. 82. 83. 84. 85. 86. 87. 88. 89.

=1/6 =1/15 1/1326 1/1326 1/120 240/11880=2/99 192/132600=8/5525 5040/362880=1/72 3/216=1/72

90. 60/165=