ACT Math — Statistics & Probability Domain Test

Calculator is allowed on all questions. Figures are not necessarily drawn to scale.

Question 1

The numbers of pages read by 5 students are 18, 24, 20, 16, and 22. What is the mean number of pages read?

A) 18
B) 19
C) 20
D) 21

Show solution

The sum is \(18+24+20+16+22=100\).

Divide by 5: \(100/5=20\).

Answer: C

Question 2

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If 1 marble is selected at random, what is the probability that it is blue?

F) \(\frac{1}{5}\)
G) \(\frac{3}{10}\)
H) \(\frac{1}{3}\)
J) \(\frac{3}{5}\)

Show solution

Use \(P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}\).

There are \(5+3+2=10\) marbles and 3 are blue, so \(P(\text{blue})=\frac{3}{10}\).

Answer: G

Question 3

For the data set 4, 7, 9, 11, 15, what is the median?

A) 7
B) 8
C) 9
D) 11

Show solution

The values are already ordered.

The middle of the 5 values is 9.

Answer: C

Question 4

The table shows whether 60 students play a school sport. How many of the students do not play a school sport?

	Plays a sport	Does not play a sport	Total
Grade 9	18	12	30
Grade 10	15	15	30
Total	33	27	60

F) 15
G) 27
H) 30
J) 33

Show solution

The total in the “Does not play a sport” column is 27.

Answer: G

Question 5

The temperatures, in degrees Fahrenheit, recorded over 5 mornings were 61, 66, 64, 70, and 63. What is the range of the temperatures?

A) 7
B) 8
C) 9
D) 10

Show solution

The range is the maximum minus the minimum: \(70-61=9\).

Answer: C

Question 6

A course grade is based on homework worth 40% and exams worth 60%. A student has a homework average of 90 and an exam average of 80. What is the student’s course average?

F) 82
G) 84
H) 86
J) 88

Show solution

Compute the weighted average: \(0.40(90)+0.60(80)=36+48=84\).

Answer: G

Question 7

The probability that a randomly selected light bulb is defective is 0.04. What is the probability that it is not defective?

A) 0.04
B) 0.40
C) 0.94
D) 0.96

Show solution

The probabilities of complementary events sum to 1: \(1-0.04=0.96\).

Answer: D

Question 8

Which description best matches the association shown in the scatterplot?

F) Positive association
G) Strong negative association
H) Weak negative association
J) No association

Show solution

As \(x\) increases, the plotted values of \(y\) generally increase.

This indicates a positive association.

Answer: F

Question 9

A café offers 3 types of bread and 4 sandwich fillings. If a customer chooses 1 type of bread and 1 filling, how many different sandwiches are possible?

A) 7
B) 12
C) 16
D) 24

Show solution

By the multiplication principle, there are \(3\times4=12\) possible sandwiches.

Answer: B

Question 10

The boxplot summarizes a data set. What is the interquartile range of the data?

F) 15
G) 20
H) 25
J) 40

Show solution

The interquartile range is \(Q_3-Q_1=45-20=25\).

Answer: H

Question 11

A fair coin is flipped twice. What is the probability that both flips are heads?

A) \(\frac{1}{4}\)
B) \(\frac{1}{3}\)
C) \(\frac{1}{2}\)
D) \(\frac{3}{4}\)

Show solution

The flips are independent: \(P(\text{HH})=\frac12\cdot\frac12=\frac14\).

Answer: A

Question 12

A student’s final grade is determined by quizzes worth 25%, a project worth 35%, and an exam worth 40%. The student earns 88 on quizzes, 92 on the project, and 80 on the exam. What is the final grade?

F) 84.0
G) 85.5
H) 86.2
J) 87.0

Show solution

The weighted grade is \(0.25(88)+0.35(92)+0.40(80)=22+32.2+32=86.2\).

Answer: H

Question 13

Which data set has the greatest standard deviation?

A) \(\{5,5,5,5,5\}\)
B) \(\{3,4,5,6,7\}\)
C) \(\{1,3,5,7,9\}\)
D) \(\{-5,0,5,10,15\}\)

Show solution

Standard deviation measures spread.

Choice D has values spread farthest from their mean.

it has the greatest standard deviation.

Answer: D

Question 14

A box contains 4 black pens and 6 blue pens. Two pens are selected at random without replacement. What is the probability that both pens are black?

F) \(\frac{1}{15}\)
G) \(\frac{2}{15}\)
H) \(\frac{1}{5}\)
J) \(\frac{4}{25}\)

Show solution

The first black pen has probability \(\frac4{10}\).

Then 3 black pens remain among 9 pens: \(\frac4{10}\cdot\frac3{9}=\frac{2}{15}\).

Answer: G

Question 15

The table summarizes transportation choices for 100 students. If a student who uses the bus is selected at random, what is the probability that the student is in Grade 12?

	Uses bus	Does not use bus	Total
Grade 11	24	16	40
Grade 12	18	42	60
Total	42	58	100

A) \(\frac{3}{10}\)
B) \(\frac{3}{7}\)
C) \(\frac{7}{10}\)
D) \(\frac{18}{100}\)

Show solution

Among the 42 students who use the bus, 18 are in Grade 12.

Thus the conditional probability is \(\frac{18}{42}=\frac37\).

Answer: B

Question 16

A 4-digit code is formed using the digits 1, 2, 3, 4, and 5, with no digit repeated. How many different 4-digit codes can be formed?

F) 20
G) 60
H) 120
J) 625

Show solution

There are 5 choices for the first digit, then 4, then 3, then 2.

Thus \(5\cdot4\cdot3\cdot2=120\).

Answer: H

Question 17

The graph shows average scores of 94 for Group A and 98 for Group B. Which feature of the graph most exaggerates the visual difference between the groups?

A) The vertical axis begins at 90 instead of 0.
B) The bars have equal widths.
C) The groups are shown with separate bars.
D) The horizontal axis names the groups.

Show solution

Because the vertical axis begins at 90, a 4-point difference occupies a large fraction of the displayed scale, making the difference look much larger than it is.

Answer: A

Question 18

A line of best fit for a data set is \(y=2.4x+7.5\). According to this model, what value of \(x\) corresponds to a predicted value of \(y=39.9\)?

F) 11.5
G) 12.5
H) 13.5
J) 14.5

Show solution

Set \(39.9=2.4x+7.5\): then \(32.4=2.4x\).

\(x=13.5\).

Answer: H

Question 19

A committee of 3 people is selected from 5 teachers and 4 students. If the committee must contain exactly 2 teachers and 1 student, how many different committees are possible?

A) 20
B) 30
C) 40
D) 60

Show solution

Choose 2 of the 5 teachers and 1 of the 4 students: \(\binom52\binom41=10\cdot4=40\).

Answer: C

Question 20

A study finds that students who report more hours of sleep tend to have higher test scores. Which conclusion is best supported by this finding?

F) More sleep definitely causes higher test scores.
G) Higher test scores cause students to sleep more.
H) Sleep and test scores cannot be related because other variables may exist.
J) There is an association between sleep and test scores, but the study alone does not establish causation.

Show solution

The finding establishes an association, but without a controlled design it does not by itself show that sleep causes the higher scores.

Answer: J