Download Sample Questions for Mastery #3

Name: ________________________ Class: ___________________ Date: __________
ID: A
Sample Questions for Mastery #3
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
____
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
d. 13.25
b. 10.25
____
3. Which of the following describes the histogram of a perfectly U-shaped distribution?
a. assymetric
c. skewed
b. bars of equal height
d. bimodal
____
4. The histogram of a U-shaped distribution may have an interval with frequency zero located
a. in the middle
c. only on the right side
b. only on the left side
d. on both the left and right sides
____
5. 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
____
6. Which of the following distributions is not symmetrical?
a. U-shaped
c. mound-shaped
b. uniform
d. skewed
____
7. 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
____
8. 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
____
9. What shape of distribution best describes the following data?
Score
Frequency
a.
b.
U-shaped
uniform
10
102
11
118
12
122
13
119
c.
d.
1
mound-shaped
skewed
Name: ________________________
ID: A
____ 10. The average IQ is 100 and most people have an IQ between 90 and 110. Very few people have an IQ below 55
or above 145. The distribution of IQs is most likely
a. U-shaped
c. mound-shaped
b. uniform
d. skewed
____ 11. What term describes the following data?
Score
Frequency
a.
b.
0
12
1
8
2
6
right-skewed
left-skewed
3
2
4
1
c.
d.
symmetric
bimodal
____ 12. The men that shop for clothes at the Hard-to-Fit Shoppe are typically unusually short or unusually tall. The
distribution of their heights is likely to be
a. U-shaped
c. mound-shaped
b. uniform
d. skewed
____ 13. 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
____ 14. 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
____ 15. 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
____ 16. What measure of central tendency is most appropriate to determine the winner of the election for the student
council president if each student picks one candidate?
a. mean
c. mode
b. median
d. weighted mean
____ 17. What is the mean mass (in grams) of the screws with masses as tabulated below?
Mass (g)
Frequency
a.
b.
8.0
8.25
7.0
1
7.5
2
8.0
7
c.
d.
2
8.3
8.5
8.5
4
9.0
6
Name: ________________________
ID: A
____ 18. Find the mean engine displacement (in cubic centimetres) for the cars in a parking lot.
Displacement (cm3)
Frequency
a.
b.
1000–2000
8
2000–3000
10
2000
2040
c.
d.
3000–4000
5
4000–5000
2
2500
2540
____ 19. What is the modal interval for the sprint times (in seconds) tabulated below?
Time (s)
Frequency
a.
b.
9.80-9.89
9.90-9.99
9.80–9.89
2
9.90–9.99
4
10.00–10.09
6
c.
d.
10.10–10.19
8
10.00-10.09
10.10-10.19
____ 20. 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
____ 21. 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
____ 22. 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
____ 23. 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
____ 24. 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
____ 25. The median mass of a collection of 8 oranges, some of which have the same mass, is 200 g. If a ninth orange
heavier than all the others is added to the collection, what effect will it have on the median?
a. cannot be determined
c. it will be unchanged
b. it will increase
d. it will decrease
____ 26. The modes of the years of teaching experience for the 11 teachers in a mathematics department are 4 and 7
years. What will the modes be after each of these teachers has 2 more years teaching experience?
a. cannot be determined
c. 4 and 9
b. 6 and 7
d. 6 and 9
3
Name: ________________________
ID: A
____ 27. Sam observed that after one positive number in a certain data set was changed to zero only one of the mean,
median, and mode changed. Which one was it?
a. cannot be determined
c. median
b. mean
d. mode
____ 28. Find the range of the following set of data: 3, −4, 0, 5, −2, 8
a. 4
c. 8
b. 5
d. 12
____ 29. Find Q3 for the following masses of students in kilograms: 70, 74, 78, 80, 81, 84, 90, 92, 94
a. 87
c. 91
b. 90
d. 92
____ 30. Find the interquartile range of the following Scrabble scores: 120, 150, 201, 185, 201, 162, 210
a. 12
c. 90
b. 51
d. 15
____ 31. 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
____ 32. A data set has a mean of 10 and a variance of 4. What is the standard deviation?
a. 2
c. 6
b. 4
d. 10
____ 33. Find the first quartile for the numbers of children in twenty families:
Number of Children
Frequency
a.
b.
0
1
1
4
2
7
1
1.5
3
5
c.
d.
4
1
5
2
2
2.5
____ 34. Find the interquartile range of the annual number of traffic fatalities on an expressway for the last twenty-five
years.
Number of Fatalities
Frequency
a.
b.
2
2.5
0
7
1
8
2
4
c.
d.
4
3
4
3
5
4
1
5
1
Name: ________________________
ID: A
____ 35. State the standard deviation of the numbers of taxi passengers to the nearest decimal place.
Number of Passengers
Frequency
a.
b.
0.8
0.9
1
24
2
14
3
10
c.
d.
4
2
1.0
1.1
____ 36. Using the interquartile range which student’s quiz marks are more consistent?
Adam: 14, 15, 17, 20
Anne: 14, 14, 17, 19
a. Adam’s
c. they are equally consistent
b. Anne’s
d. cannot be determined
____ 37. Use the standard deviation to determine which of the two baseball teams has been more consistent in its scoring
for the last five games.
N.Y: 0, 4, 2, 3, 6
St.L: 1, 3, 3, 5, 7
a. N.Y
c. they are equally consistent
b. St.L
d. it cannot be determined
____ 38. 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
____ 39. 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
____ 40. A set of five different whole numbers is arranged in order from smallest to largest. The third number is then
decreased by one. Which measure of spread for the set could this change?
a. the range
c. the standard deviation
b. the IQR
d. all of the above
____ 41. Stephen used a measure of spread to conclude that the movie ticket prices (in $) in set A were more spread out
than those in set B. Which measure of spread did he use?
A: 10, 11, 11, 13, 15
B: 10, 11, 13, 13, 15
a. the range
c. the standard deviation
b. the IQR
d. none of the above
____ 42. Which of the following measures of spread could be negative?
a. the range
c. the standard deviation
d. none of the above
b. the IQR
5
Name: ________________________
ID: A
____ 43. Which of the following is not an example of a discrete random variable?
a. the number of heads observed for ten coin tosses
b. the mass of an apple randomly chosen from a supermarket bin
c. the sum resulting from the roll of two six-sided dice
d. the number of hearts in a randomly chosen hand of seven playing cards
____ 44. A tetrahedron has four equal triangular faces. The faces of a tetrahedral die are labelled with the numbers one,
three, five, and seven. What is the expected value of the random variable representing the number observed on a
single roll of this die?
a. 3
c. 4
b. 3.5
d. 5
____ 45. What is the probability of a sum of 5 resulting from the roll of two six-sided dice?
5
1
a.
c.
36
18
1
1
b.
d.
9
36
____ 46. When we compare the possible values for a discrete random variable to its expected value, the following
statement must be true.
a. The possible values and the expected value must all be whole numbers.
b. The expected value must be one of the possible values.
c. The possible values must all be whole numbers but the expected value may be a rational
number.
d. The expected value will not be a whole number.
____ 47. The probability of drawing a red card from a deck of 52 playing cards is 0.5. Which of the following
statements is not necessarily true?
a. The expected value for the number of red cards in a 7 card hand will be 3.5.
b. Over many repeated drawings you would expect the ratio of red cards drawn to total
number of drawings to be close to 1:2.
c. The expected value for the number of black cards in an 8 card hand will be 4.
d. If you successively draw and replace a card 100 times, you will see 50 red cards.
____ 48. What is the probability of rolling less than 3 on a single roll of a six-sided die?
1
1
a.
c.
3
6
1
2
b.
d.
2
3
6
Name: ________________________
ID: A
____ 49. A game is played by spinning a wheel that is divided into four sectors, each with a different point value. The
central angle and point value for each sector is shown in the chart below.
Central Angle
144°
108°
72°
36°
Point Value
20
30
40
50
How many total points would you expect to get for 100 spins of the wheel?
a. 3500
c. 2500
b. 3000
d. 2000
____ 50. Which of the following is an example of a discrete random variable?
a. the time needed by a student to complete a physics lab
b. the number of red cars observed in a student parking lot
c. the mass of a green pepper selected at random from a bin
d. the cost of a U.S. dollar in Canadian currency on a given day
____ 51. The following table shows the probability distribution for the possible sums that result from rolling two 6-sided
dice.
X
1
P(X)
0
X
7
P(X)
6
8
36
5
2
1
3
36
2
9
36
4
4
36
3
10
36
3
5
36
4
11
36
2
6
36
5
12
36
1
36
36
What is the probability that the sum rolled is even and less than 9?
7
1
a.
c.
18
9
5
1
b.
d.
36
2
7
Name: ________________________
ID: A
____ 52. What is the probability of drawing exactly 2 red cards in a hand of 3 cards drawn from a deck of 52 cards?
1
2
a.
c.
8
3
1
3
b.
d.
2
8
____ 53. A game involves tossing three coins. If two or more of the coins are heads, the player wins a prize. Each play
costs $0.25. What value of prize will make this a fair game?
a. $0.40
c. $0.45
b. $0.50
d. $0.38
____ 54. The following table is a valid probability distribution for a random variable X. What must be the value for P(2)
to complete the table?
X
0
1
2
3
a.
b.
P(X)
0.15
0.2
0.4
0.15
0.2
c.
d.
0.25
0.3
____ 55. A random variable X is defined as the number of heads observed when a coin is tossed 4 times. The probability
distribution for this random variable is shown below.
X
P(X)
0
1
1
4
2
6
3
4
4
1
16
16
16
16
16
Which of the following statements is not true?
a. The probability of no heads is the same as the probability of 4 heads.
b. The most likely outcome is 2 heads.
6
c. The expected value is .
16
d. The probability of not tossing 2 heads is greater than the probability of tossing 2 heads.
____ 56. What is the expected value for a single roll of a 6-sided die?
a. 3.5
c. 4
1
b. 3
d.
6
8
Name: ________________________
ID: A
____ 57. A student is preparing a probability distribution as shown below.
X
0
1
2
3
4
P(X)
0.3
0.3
0.3
0.3
A value is needed for P(3) to complete the table. Which statement below is true?
a. The required value for P(3) is 0.3.
b. The required value for P(3) is 0.2.
c. The required value for P(3) is –0.2.
d. There is no possible value for P(3) that can make this a valid probability distribution.
ÊÁ ˆ˜
ÁÁ n ˜˜
____ 58. According to Pascal’s Identity, the single expression of the form ÁÁÁÁ ˜˜˜˜ , which is equivalent to
ÁÁ ˜˜
Ër¯
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 11 ˜˜
ÁÁ 12 ˜˜
Á
˜
a. ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜
ÁÁ ˜˜
Ë 5¯
Ë 4¯
ÊÁ ˆ˜
ÊÁ
ˆ
ÁÁ 12 ˜˜
ÁÁ 121 ˜˜˜
Á
˜
Á
˜˜
b. ÁÁÁ ˜˜˜
d. ÁÁÁ
˜˜˜
ÁÁ ˜˜
ÁÁ
˜
3
12
Ë ¯
Ë
¯
ÁÊÁ ˜ˆ˜
Á8˜
____ 59. According to Pascal’s Identity, what two expressions may be added to obtain ÁÁÁÁ ˜˜˜˜ ?
ÁÁ ˜˜
Ë6¯
ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 4 ˜˜ ÁÁ 4 ˜˜
ÁÁ 8 ˜˜ ÁÁ 8 ˜˜
Á
˜
Á
˜
a. ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë3¯ Ë3¯
Ë4¯ Ë5¯
ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 7 ˜˜ ÁÁ 7 ˜˜
ÁÁ 7 ˜˜ ÁÁ 7 ˜˜
Á
˜
Á
˜
b. ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜
d. ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë5¯ Ë6¯
Ë4¯ Ë5¯
7
____ 60. How many terms are in the expansion of ÊÁË 2x − 3y ˆ˜¯ ?
a. 5
c. 7
b. 8
d. 6
5
____ 61. In the expansion of ÊÁË x + y ˆ˜¯ , what is the coefficient of the fourth term?
a. 10
c. 7
b. 4
d. 5
9
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 11 ˜˜ ÁÁ 11 ˜˜
ÁÁ ˜˜ + ÁÁ ˜˜ ?
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë 3¯ Ë 4¯
Name: ________________________
ID: A
n
____ 62. In the expansion of ÊÁË x + y ˆ˜¯ , which term or terms must have coefficients with a value of n?
a. none
c. the middle term or middle two terms
b. the second term
d. the second and second from last terms
ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜
____ 63. What is the value of ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ?
ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
Ë 0¯ Ë 1¯ Ë 2¯ Ë 3¯ Ë 4¯ Ë 5¯
a. 30
c. 32
b. 64
d. 20
____ 64. In the expansion of (a + b ) , what is the value of the exponent k in the term that contains a 5 b k ?
a. 5
c. 4
b. 56
d. 3
8
ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ n ˜˜ ÁÁ n ˜˜ ÁÁ n ˜˜ ÁÁ n ˜˜
ÁÁ n ˜˜
Á
˜
Á
˜
Á
˜
Á
˜
____ 65. If ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ +. . .+ ÁÁÁÁ ˜˜˜˜ = 64, what is the value of n?
ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜
Ë 0¯ Ë 1¯ Ë 2¯ Ë 3¯
Ën¯
a.
b.
6
8
c.
d.
4
5
____ 66. What is the coefficient of the third term in the expansion of (3x + 1) ?
a. 10
c. 150
b. 15
d. 270
5
ÊÁ ˆ˜
ÁÁ 5 ˜˜
r
5−r
____ 67. ÁÁÁÁ ˜˜˜˜ (2x) ÁÊË y ˜ˆ¯ is the general term in the expansion of which binomial power?
ÁÁ ˜˜
Ër¯
a.
b.
ÊÁ 2x − y ˆ˜ r
Ë
¯
5
ÁËÊ 2x + y ˜¯ˆ
c.
d.
5
ÁËÊ 2x − y ˜¯ˆ
r
ÁËÊ 2x + y ˜¯ˆ
____ 68. Pascal’s Triangle can be arranged into the following format.
n=0
n=1
n=2
n=3
n=4
r=0
1
1
1
1
1
r=1
r=2
r=3
r=4
1
2
3
4
1
3
6
1
4
1
Which of the following statements is not true?
a. The sum of the nth row must be 2 n .
b. The value in any cell is the sum of the cell directly above and the cell above and one left.
c. Values in each row must alternate between even and odd numbers.
d. In any row for which n is prime, all values in the row other than the first and last must be
divisible by n.
10
Name: ________________________
ID: A
6
____ 69. For the expansion of ÊÁË 3x + y ˆ˜¯ , which statement is not true?
a. The coefficient of the term containing y 6 is one.
b. The coefficient of the second term is equal to the coefficient of the fifth term.
c. The degree of each term in the expansion is 6.
d. There are seven terms in the expansion.
ÁÊÁ
____ 70. What is the value of the constant term in the expansion of ÁÁÁÁ x 2 +
ÁË
a. 4
c. 16
b. 8
d. 32
6
2 ˜ˆ˜˜
˜˜ ?
x ˜˜¯
____ 71. How many different paths will spell the word CASH using the diagram below?
C
A A
S S S
H H H H
a.
b.
6
4
c.
d.
8
10
____ 72. Which of the following is a correct expression of Pascal’s Identity?
ÁÊÁ
˜ˆ ÁÊ
˜ˆ ÁÊ ˜ˆ
ÁÊÁ
˜ˆ ÁÊ
˜ˆ ÁÊ ˜ˆ
ÁÁ n − 2 ˜˜˜ ÁÁÁ n − 1 ˜˜˜ ÁÁÁ n ˜˜˜
ÁÁ n − 1 ˜˜˜ ÁÁÁ n − 1 ˜˜˜ ÁÁÁ n ˜˜˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜˜ = ÁÁ ˜˜
a. ÁÁ
c. ÁÁ
˜˜ + ÁÁ
˜˜ = ÁÁ ˜˜
˜˜ + ÁÁ
˜˜ ÁÁ ˜˜
ÁÁ
˜˜ ÁÁ
˜˜ ÁÁ ˜˜
ÁÁ
˜˜ ÁÁ
˜ Á ˜
Ë r−2¯ Ë r−1 ¯ Ë r ¯
Ë r−1¯ Ë r ¯ Ë r ¯
ÊÁ
ˆ Ê
ˆ Ê
ˆ
ÊÁ ˆ˜ ÊÁ
ˆ Ê
ˆ
ÁÁ n + 1 ˜˜˜ ÁÁÁ n + 1 ˜˜˜ ÁÁÁ n + 2 ˜˜˜
ÁÁ n ˜˜ ÁÁ n ˜˜˜ ÁÁÁ n + 2 ˜˜˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜˜
b. ÁÁÁ
d. ÁÁÁ ˜˜˜ + ÁÁÁ
˜˜˜ + ÁÁÁ
˜˜˜ = ÁÁÁ
˜˜˜
˜˜˜ = ÁÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
˜˜ ÁÁ
˜˜
ÁÁ ˜˜ ÁÁ
˜˜ ÁÁ
˜˜
r
−
1
r
r
+
1
r
r
+
1
r
+
1
Ë
¯ Ë
¯ Ë
¯
Ë ¯ Ë
¯ Ë
¯
____ 73. Which of the following is not a property of a Binomial Experiment?
a. All trials are identical.
b. Each trial has only two possible outcomes.
c. The probability of success may change from trial to trial.
d. The purpose of the experiment is to determine the number of successes that occurs during
the n trials.
____ 74. Which of the following is not an example of a Bernoulli Trial?
a. A coin is tossed 20 times and the number of heads is recorded.
b. A container contains 49 numbered balls. Six are drawn one at a time from the container.
c. A couple produces 18 children. The number of female children is recorded.
d. A batter has a lifetime average of .300. The number of hits in 5 successive at-bats is
recorded.
11
Name: ________________________
ID: A
ÁÊÁ ˜ˆ˜
Á 8˜
3
5
____ 75. In the expression ÁÁÁÁ ˜˜˜˜ (0.2) (0.8) , which value represents the number of trials?
ÁÁ ˜˜
Ë 3¯
a. 2
c. 5
b. 3
d. 8
ÊÁ ˆ˜
ÁÁ 7 ˜˜
2
5
____ 76. In the expression ÁÁÁÁ ˜˜˜˜ (0.4) (0.6) , which value represents the probability of failure?
ÁÁ ˜˜
Ë 2¯
a.
b.
0.6
0.4
c.
d.
(0.4)2
(0.6)5
ÊÁ ˆ˜
ÁÁ 10 ˜˜
3
7
____ 77. In the expression ÁÁÁÁ ˜˜˜˜ (0.5) (0.5) , which value represents the number of successes?
ÁÁ ˜˜
Ë 3¯
a. 3
c. 5
b. 10
d. 7
____ 78. Which expression describes the probability of k “3s” being rolled on 20 successive rolls of a six-sided die?
ÁÊÁ ˜ˆ˜ ÁÊ 1 ˜ˆ k ÁÊ 5 ˜ˆ 20 − k
ÁÊÁ ˜ˆ˜ ÁÊ 3 ˜ˆ k ÁÊ 3 ˜ˆ 20 − k
ÁÁ 20 ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
Á 20 ˜ Á ˜ Á ˜
Á
˜
a. ÁÁ ˜˜ ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
Ë k ¯Ë ¯ Ë ¯
Ë k ¯Ë ¯ Ë ¯
ÊÁ ˆ˜ Ê ˆ k Ê ˆ 20 − k
ÊÁ ˆ˜ Ê ˆ 3 Ê ˆ 17
ÁÁ 20 ˜˜ ÁÁ 5 ˜˜ ÁÁ 1 ˜˜
ÁÁ 20 ˜˜ ÁÁ 1 ˜˜ ÁÁ 5 ˜˜
Á
˜
Á
˜
Á
˜
b. ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜
d. ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
Ë k ¯Ë ¯ Ë ¯
Ë 3 ¯Ë ¯ Ë ¯
____ 79. A baseball player hits the ball to left field 20% of the time, to centre field 35% of the time, and to right field
45% of the time. Which of the following expressions gives the probability distribution for the number of hits to
centre field for a game in which the batter gets 5 hits?
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 5 ˜˜
ÁÁ 5 ˜˜
k
5 −k
k
5−k
Á
˜
c. ÁÁÁÁ ˜˜˜˜ (0.35) (0.65)
a. ÁÁÁ ˜˜˜ (0.2) (0.8)
ÁÁ ˜˜
ÁÁ ˜˜
Ëk ¯
Ëk ¯
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 5 ˜˜
ÁÁ 5 ˜˜
k
5−k
k
5−k
Á
˜
b. ÁÁÁ ˜˜˜ (0.65) (0.35)
d. ÁÁÁÁ ˜˜˜˜ (0.45) (0.55)
ÁÁ ˜˜
ÁÁ ˜˜
Ëk ¯
Ëk ¯
____ 80. The probability of a computer memory chip being defective is 0.02. Which of the following statements is true?
a. In a shipment of 100 chips, two will be defective.
b. The expected number of defective chips in a shipment of 500 is ten.
c. In a shipment of 1000 chips, it is certain that at least one will be defective.
d. All statements above are false.
____ 81. A young couple plans to have a family with four children. Assuming that the behaviour of their first child does
not cause them to alter their plans, what is the expected number of girls for their family?
a. 2.5
c. 2
b. 2.25
d. 1.5
12
Name: ________________________
ID: A
____ 82. The probability of success for a binomial experiment is greater than 0.5. Which is the most accurate description
of the graph of its probability distribution?
a. symmetrical
c. highest point is right of centre
b. highest point is left of centre
d. all bars have equal height
____ 83. What is the smallest p value that will give a probability of at least 0.5 that an experiment will be successful
four times in four trials?
1
a.
c. 0.9
16
b.
0.85
d.
1
4
2
____ 84. A young couple hopes to have two children. They would like the first to be a boy and the second to be a girl.
What is the probability that their first two children will arrive as described?
a. 0
c. 0.5
b. 0.25
d. 0.75
ÊÁ ˆ˜
ÁÁ 6 ˜˜
2
4
____ 85. In the expression ÁÁÁÁ ˜˜˜˜ (0.1) (0.9) , which value represents the number of failures?
ÁÁ ˜˜
Ë 2¯
a.
b.
6
2
c.
d.
4
1
____ 86. Which statement regarding the probability distribution for a binomial experiment with p = 0.5 is not true?
a. The probability of no successes must equal the probability of no failures.
b. The graph of the distribution is symmetrical.
c. The expected value of the experiment is half the number of trials.
d. The more trials that are made, the higher the probability that all trials will be successful.
____ 87. A student suggests the following expression to represent the probability of achieving four successes in seven
trials of a binomial experiment for which the probability of success is 0.3.
ÊÁ ˆ˜
ÁÁ 7 ˜˜
ÁÁ ˜˜ (0.3) 4 (0.4) 3
ÁÁ ˜˜
ÁÁ ˜˜
Ë 4¯
What error did the student make?
a. The second exponent should be a 7.
b. The probabilities for success and failure were reversed from their proper positions.
c. The probability of failure should be 0.7.
d. The first exponent should be a 7.
Short Answer
88. State the mean and median for the data set {2, 5, 7, 1, 3}.
89. State the median and mode(s) for the following CD prices:
$12, $14, $15, $12, $14, $17, $16, $19
13
Name: ________________________
ID: A
90. 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.
91. Find the range of the following data set: 2, 7, 0, −1, 5, 9
92. State the first and third quartiles for the bus stop waiting times in minutes: 10, 5, 7, 6, 7, 5, 4, 12
93. What is the interquartile range for the following average January temperatures (in °C): −2.0, −1.5, 0.2, 1.7,
2.6, 4.1, 4.1, 5.0, 7.2, 8.1, 8.1
94. The variance of a set of data is 13.2. Find the standard deviation to one decimal place.
95. A hockey goaltender has a save percentage of 0.920. This means that the probability of any single shot taken on
the goaltender being a goal is 0.08. What would be the expected number of goals scored on this goaltender in a
game where she faced 35 shots?
ÊÁ ˆ˜
ÁÁ 5 ˜˜
3
2
96. Fully describe the probability that is expressed by ÁÁÁÁ ˜˜˜˜ (0.2) (0.8) .
ÁÁ ˜˜
Ë 3¯
ÊÁ ˆ˜ Ê ˆ 4 ÊÁ ˆ˜ Ê ˆ 1 Ê ˆ 3 ÊÁ ˆ˜ Ê ˆ 2 Ê ˆ 2 ÊÁ ˆ˜ Ê ˆ 3 Ê ˆ 1 ÊÁ ˆ˜ Ê ˆ 4
ÁÁ 4 ˜˜ ÁÁ 4 ˜˜
ÁÁ 4 ˜˜ ÁÁ 1 ˜˜ ÁÁ 4 ˜˜
ÁÁ 4 ˜˜ ÁÁ 1 ˜˜ ÁÁ 4 ˜˜
ÁÁ 4 ˜˜ ÁÁ 1 ˜˜ ÁÁ 4 ˜˜
ÁÁ 4 ˜˜ ÁÁ 1 ˜˜
97. Evaluate ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ .
ÁÁ ˜˜ Á 5 ˜
ÁÁ ˜˜ Á 5 ˜ Á 5 ˜
ÁÁ ˜˜ Á 5 ˜ Á 5 ˜
ÁÁ ˜˜ Á 5 ˜ Á 5 ˜
ÁÁ ˜˜ Á 5 ˜
Ë 0¯Ë ¯
Ë 1¯Ë ¯ Ë ¯
Ë 2¯Ë ¯ Ë ¯
Ë 3¯Ë ¯ Ë ¯
Ë 4¯Ë ¯
98. A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. What
is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective?
99. A fair die has four faces numbered one to four. What is the probability of rolling a two exactly three times in
ten rolls of the die?
14
ID: A
Sample Questions for Mastery #3
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.
B
A
D
A
B
D
C
D
B
C
A
A
D
A
B
C
C
D
D
B
C
C
A
D
A
D
B
D
C
B
A
A
B
B
B
C
C
C
1
ID: A
39.
40.
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.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
D
C
C
D
B
C
B
C
D
A
B
B
A
D
B
C
C
A
D
C
B
B
A
D
C
D
A
D
B
C
B
C
C
C
C
A
D
A
A
A
C
B
C
C
2
ID: A
83.
84.
85.
86.
87.
A
B
C
D
C
SHORT ANSWER
88.
89.
90.
91.
92.
93.
94.
95.
96.
The mean is 3.6 and the median is 3.
The median CD price is $14.50 and the two modes are $12 and $14.
Alfredo’s final mark is 73.
The range is 10.
The first quartile is 5 minutes and the third quartile is 8.5 minutes.
The average January temperature is 7.0ºC.
The standard deviation is 3.6.
2.8 goals
For a binomial experiment with a probability of success of 0.2 for any single trial, this expression gives the
probability of three successes in five trials.
97. 1
98. 0.169
99. 0.2503
3