WorksheetsProbability and Statistics Quiz
Total questions: 62
Worksheet time: 34mins
A survey was taken of children between the ages of 3 and 7. Let A be the event that the person has 2 siblings, and let B be the event that the person does not have a pet. Which statement is true about whether A and B are independent events?
A and B are independent events because P(A∣B) = P(A) = 0.18.
A and B are independent events because P(A∣B) = P(A) = 0.4.
A and B are not independent events because P(A∣B) = 0.4 and P(A) = 0.18.
A and B are not independent events because P(A∣B) = 0.18 and P(A) = 0.4.
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot. What is the probability that a randomly selected car with no 4-wheel drive has third-row seats?
0.3
0.4
0.7
0.8
People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events 'prefers pink lemonade' and 'female' are independent because
P(pink lemonade | female) = P(pink lemonade) = 0.6.
P(female | pink lemonade ) = P(pink lemonade) = 0.3.
P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6.
P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.
Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team members who do not wear glasses, 30 percent of them are in the 10th grade. To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?
14%
17%
55%
67%
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8. Why are the events not mutually exclusive?
The sum of P(A) and P(B) is less than P(A or B).
The product of P(A) and P(B) is less than P(A or B).
The product of P(A) and P(B) is not equal to P(A or B).
The sum of P(A) and P(B) is not equal to P(A or B).
A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. What is the probability that a student chooses drama as an elective?
5 percent
7 percent
33 percent
37 percent
Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last skater. Then, they try to decide whether or not Oliver should be the first skater in the race. Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race?
A = {MOPN, PMON}
A = {OPMN, OMPN}
A = {MOPN, MPON, OPMN, POMN}
A = {MOPN, MPON, PMON, POMN}
A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probability that the committee consists of all boys?
4/1001
15/1001
10/143
133/143
Iliana is painting a picture. She has green, red, yellow, purple, orange, and blue paint. She wants her painting to have four different colors. If order does not matter, in how many ways can she pick four colors if green must be one of them?
4
6
10
15
Including Jose, there are eight people in his family. If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?
35
840
1,680
2,620
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?
yes, because all the elements of set A are in set R
yes, because all the elements of set R are in set A
no, because each element in set A is not represented in set R
no, because each element in set R is not represented in set A
The Venn diagram shows the number of employers who ranked skills important for careers in their field. C represents communication, T represents technical skills, and M represents the ability to handle money. How many employers ask that employees be skilled in communication and handling money?
47
50
67
86
The frequency table represents the results of a survey comparing the average age of household members to the way that they watch non-network television. Madigan converts the frequency table to a conditional relative frequency table by row. Television Viewing Method Which value should she use for X? Round to the nearest hundredth.
0.09
0.20
0.25
0.30
Given that a child spends at least 1 hour per day outside, what is the probability, rounded to the nearest hundredth if necessary, that the child spends less than 1 hour per day on electronics?
0.22
0.25
0.70
0.88
Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent.
8%
21%
33%
38%
Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent.
18%
22%
35%
82%
Which sample fairly represents the population? Select two options.
using a yearbook to determine the most popular names for girls in the United States
asking the people exiting a vitamin store how often they exercise to determine the amount of time the average American exercises
calling every registered member of the national Republican Party to determine the voter turnout for a city’s mayoral race
sending a mandatory and confidential e-mail survey to every tenth employee of a company to determine overall job satisfaction
taking a poll in the main hallway between classes to determine the number of students who would be interested in a school trip to New York City
Which represents the solution(s) of this system of equations? y = –x^2 – 2x + 8 and y = 2x + 11
(–3, –1)
(–3, 5)
(–3, 5) and (–1, 9)
(1, 13) and (3, 20)
Which represents the solution(s) of the system of equations, y = x^2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically.
(–5, –80)
(5, 0)
(5, 0) and (–5, –80)
no solutions
Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg. Which equation can be used to find x, the length of the shorter leg?
x(x + 7) = 13
x(x + 7) = 169
x^2 + (x + 7)^2 = 13
x^2 + (x + 7)^2 = 169
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
0 = –4.9t^2 + 19.6t + 24.5
0 = –4.9t^2 + 24.5t + 19.6
19.6 = –4.9t^2 + 24.5t
24.5 = –4.9t^2 + 19.6t
Joline is solving the equation 0 = x^2 – 5x – 4 using the quadratic formula. Which value is the negative real number solution to her quadratic equation? Round to the nearest tenth if necessary.
–5.7
–4
–1
–0.7
What is the discriminant of the quadratic equation 2x + 5x^2 = 1?
–18
–16
22
24
Which best explains why a term is not added to the left side of the equation in the last step shown in the table?
The term is added to the right side of the equation, so it needs to be subtracted from the left side of the equation to balance the sides of the equation.
The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
The term needs to be converted so it has a common denominator before adding it to the left side of the equation to balance the equation.
The square root of the term needs to be found before adding the term to the left side of the equation to balance the sides of the equation.
Which equation has an a-value of 1, a b-value of –3, and a c-value of –5?
0 = –3x – 5 + x^2
0 = x – 3 – 5x^2
0 = 3x – 5 – x^2
0 = –3x + 5 – x^2
Which is a zero of the quadratic function f(x) = 4x^2 + 24x + 11?
x = –9.25
x = –5.5
x = 0.5
x = 3.25
Susu is solving the quadratic equation 4x^2 -8x-13=0 by completing the square. Her first four steps are shown in the table. In which step did Susu first make an error?
Step 1
Step 2
Step 3
Step 4
Solve x^2 + 12x = –11 by completing the square. Which is the solution set of the equation?
{–11, –1}
{–11, 1}
{11, –1}
{11, 1}
Solve x^2 + 10x = 24 by completing the square. Which is the solution set of the equation?
{–12, 2}
{–2, 12}
Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x + 10)^2 = 256, x represents the side measure of the original square photo. What were the dimensions of the original photo?
4 inches by 4 inches
6 inches by 6 inches
10 inches by 10 inches
12 inches by 12 inches
Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?
n^2 + n – 210 = 0
n^2 + n – 105 = 0
2n^2 + 2n + 210 = 0
2n^2 + 2n + 105 = 0
A square piece of paper has an area of x^2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units. Which equation can be used to solve for x, the side length of the original square?
x^2 − 2x − 120 = 0
x^2 + 2x − 120 = 0
x^2 − 2x + 120 = 0
x^2 + 2x + 120 = 0
The equation x^2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?
–19
–9
1
10
Which function has real zeros at x = –8 and x = 5?
g(x) = x^2 + 3x – 40
g(x) = x^2 + 3x + 40
g(x) = x^2 + 14x – 40
g(x) = x^2 + 14x + 40
The graph represents the fees in thousands of dollars, y, depending on the amount invested in millions, x, with one financial investment firm. Over what interval is the change constant?
[0, 5)
[1, 5)
[0, 20)
[1, 20)
A party planner is going to use an arch of balloons for a parade of recent graduates. The estimated curve the balloons will create is modeled by the function given in the table, where x represents the distance in feet along the ground from the start and f(x) represents the height in feet above the ground. The planner needs a clearance of 9 feet under the arch. Has the planner met the minimum height?
no, because the width of the arch is 8 feet
yes, because the width of the arch is 9.6 feet
no, because the maximum height of the arch is 8 feet
yes, because the maximum height of the arch is 9.6 feet
What are the domain and range of f(x) = |x + 6|?
domain: ; range: f(x) 0
domain: x ; range:
domain: x ; range:
domain: ; range: f(x) 0
Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?
x = –2, x = –8
x = –2, x = –6
x = –2, x = 6
x = –2, x = 8
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function?
Both the domain and range change.
Both the range and domain stay the same.
The domain stays the same, but the range changes.
The range stays the same, but the domain changes.
What is the range of the function f(x) = –2|x + 1|?
all real numbers
all real numbers less than or equal to 0
all real numbers less than or equal to 1
all real numbers greater than or equal to 1
Which graph represents the function g(x) = |x + 4| + 2?
Graph one
Graph 2
Graph 3
Graph 4
What is the vertex of the graph of f(x) = |x – 13| + 11?
(–11, 13)
(–13, 11)
(11, 13)
(13, 11)
The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in minutes spent on the Internet. Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store.
The first half hour is free, and then it costs $5 per minute to connect to the Internet.
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
Any amount of time over an hour and a half would cost $10.
Which are points on the graph of y = 1.5 + ⌈x⌉? Select three options
(–4.5, –2.5)
(–0.8, 0.5)
(7.9, 9.5)
(4.5, 6)
(1.3, 3.5)
The graph represents the data cost for monthly Internet service for a cell phone. Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month?
A function g(x) is defined as shown. What is the value of g(4)?
10
12
14
16
In general, how does the growth of y = 3x compare to the growth of y = 3^x?
The function y = 3x is growing slower than y = 3^x.
The function y = 3x is growing faster than y = 3^x.
The functions y = 3x and y = 3^x are growing at the same rate.
The function y = 3^x is growing slower than y = 3x.
Dwight creates a table of values for a function and plots the points. He finds that one y value divided by the next y value produces the same answer each time. What kind of function did he graph?
linear
quadratic
square root
exponential
The minimum of the graph of a quadratic function is located at (–1, 2). The point (2, 20) is also on the parabola. Which function represents the situation?
f(x) = (x + 1)^2 + 2
f(x) = (x – 1)^2 + 2
f(x) = 2(x + 1)^2 + 2
f(x) = 2(x – 1)^2 + 2
A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = (x – 16)(x + 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet?
0.1
0.8
1.3
1.6
What is f(x) = 7x^2 + 42x written in vertex form?
f(x) = 7(x + 6)^2 – 6
f(x) = 7(x + 6)^2 – 42
f(x) = 7(x + 3)^2 – 9
f(x) = 7(x + 3)^2 – 63
What is the axis of symmetry of h(x) = –2x^2 + 12x – 3?
x = –15
x = –3
x = 3
x = 15
The image shows a geometric representation of the function f(x) = x^2 – 2x – 6 written in standard form. What is this function written in vertex form?
f(x) = (x –1)^2 – 7
f(x) = (x +1)^2 – 7
f(x) = (x –1)^2 – 5
f(x) = (x +1)^2 – 5
What is the vertex of the function f(x) = x^2 + 12x?
(–6, –36)
(–6, 0)
(6, 0)
(6, –36)
Ali graphs the function f(x) = –(x + 2)^2 – 1 as shown. Which best describes the error in the graph?
The axis of symmetry should be x = –1.
The axis of symmetry should be x = 2.
The vertex should be a maximum.
The vertex should be (–2, 1).
Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.
Ava’s graph is a vertical translation of f(x) = x^2.
Victor’s graph is a vertical translation of f(x) = x^2.
Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.
Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.
Ava’s graph has a y-intercept of 4.
What is the midpoint of the x-intercepts of f(x) = (x – 4)(x + 4)?
(0,0)
(0,4)
(–4,0)
(2,0)
Which is the graph of f(x) = (x + 3)(x – 2)?
Graph A
Graph B
Graph C
Graph d
The graph of which function has an axis of symmetry at x = ?
f(x) = 2x^2 + x – 1
f(x) = 2x^2 – x + 1
f(x) = x^2 + 2x – 1
f(x) = x^2 – 2x + 1
The graph of which function has a minimum located at (4, –3)?
f(x) = x^2 + 4x – 11
f(x) = –2x^2 + 16x – 35
f(x) = x^2 – 4x + 5
f(x) = 2x^2 – 16x + 35
Consider the quadratic function. f(p) = p^2 – 8p – 5 What are the values of the coefficients and the constant in the function?
a = –1, b = –8, c = –5
a = 1, b = –5, c = –8
a = 1, b = –8, c = –5
a = –1, b = –5, c = 8
Which graph shows a rate of change of 1/2 between -4 and 0 on the xaxis?
Graph 1
Graph 2
Graph 3
Graph 4
