SOPHIA STATISTICS UNIT 5 PRACTICE STUDY
GUIDE 2026 QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
◉ Dropping a piece of buttered toast will theoretically land butter-
side down with a probability of 0.65. Some students decided to test
this theory and dropped five pieces of buttered toast. All five landed
butter-side down. One of the students claims that the next piece of
buttered toast dropped will land butter-side up because it is due to
happen.
Is the student's reasoning correct? Answer: B. No, the probability of
buttered toast landing butter-side down is 0.65 over a large number
of trials.
◉ A local restaurant is having a contest in which patrons spin a
wheel to win prizes. The wheel is divided into 10 identical segments,
each marked with a different prize. Seven of the segments are
labeled "Free Entree" or "Free Appetizer." The other three are
labeled "Free Valet Parking."
Let the digits 0-6 represent winning free food and 7-9 represent
winning valet parking.
Using the line of random numbers, what is the best estimate of the
number of free food prizes won by the next 20 patrons who spin the
wheel? Answer: D. 15
,◉ A study reported that about half of high school seniors study for
upcoming math tests. To find out if this applies to seniors at Garfield
High School, an SRS of 30 seniors was asked if they study for their
math tests. Nineteen responded "Yes."
A dotplot is provided showing the results of 40 trials of this
simulation.
Does this provide convincing evidence that seniors at Garfield High
School study more than the report stated? Answer: C. Yes, only one
trial had a result of 19 or larger.
◉ A contractor claims that she finishes a job on time 90% of the
time. Last month, she only completed 7 out of her 10 jobs on time.
To see if this is surprisingly low, a simulation was conducted 100
times under the assumption that she really does complete 90% of
her jobs on time.
The dotplot contains 100 trials of this simulation.
Based on this dotplot and the sample of last month's on-time
completions, which conclusion can be drawn? Answer: D. The
dotplot does not provide convincing evidence that her true, on-time
completion rate is less than 90% because 7 or fewer on-time
completions happened 19% of the time in the simulation.
,◉ A manufacturer of baseball hats claims that approximately 30% of
people regularly wear baseball hats. From a random sample of 20
students at your school, you find that only four wear baseball hats
regularly. This gives you reason to believe that the manufacturer's
claim of 30% is too high.
Let the digits 0-2 represent wearing a baseball hat (H) and the digits
3-9 represent not wearing a baseball hat (N). Use the table of
random numbers to run one trial of this simulation.
Which is the correct sequence of outcomes? Answer: A. NNNNN
HHNNN NNNHN NHNHN
◉ A teacher claims that there is a 50% chance that she will collect
homework for a grade on any given day. One week, she collected all
five daily homework assignments. A student in this class is upset and
explains that the teacher should not collect any homework
assignments the following week in order to honor her 50%
probability claim.
Is the student's reasoning correct? Answer: D. No, collecting
homework and not collecting homework are equally likely in the
long run, so whether or not the teacher collects homework on any
single day cannot be determined.
◉ Carlos thinks the traffic light to get out of his neighborhood is red
more often than green. He decides to collect data to determine the
probability of the light being red upon his approach. The graph of his
long-run relative frequencies is shown.
, Which conclusion can be drawn from this graph? Answer: B. About
63% of the time, the traffic light is red when Carlos leaves his
neighborhood.
◉ Forty percent of the beads in a bag of more than 10,000 beads are
yellow. Suzy pulls out 10 beads, one at a time with replacement, and
notes that eight of these beads are yellow. She says the next bead
pulled out will not be yellow because a yellow bead has been pulled
out too many times in a row.
Is Suzy's reasoning correct? Answer: D. No, it is true that the
probability of pulling a yellow bead is 0.40, but Suzy should not
expect that exactly 40% of such a small number of beads pulled will
be yellow.
◉ The manufacturer of a soccer ball claims that only 3% of the
soccer balls produced are faulty. An employee of this company
examines the long-run relative frequency of faulty soccer balls
produced as shown in the graph.
Which conclusion can be drawn from this graph? Answer: D. The
graph shows that the probability of producing a faulty soccer ball is
about 0.06; therefore, we should not believe the company's claim
that only 3% of the produced soccer balls are faulty.
GUIDE 2026 QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
◉ Dropping a piece of buttered toast will theoretically land butter-
side down with a probability of 0.65. Some students decided to test
this theory and dropped five pieces of buttered toast. All five landed
butter-side down. One of the students claims that the next piece of
buttered toast dropped will land butter-side up because it is due to
happen.
Is the student's reasoning correct? Answer: B. No, the probability of
buttered toast landing butter-side down is 0.65 over a large number
of trials.
◉ A local restaurant is having a contest in which patrons spin a
wheel to win prizes. The wheel is divided into 10 identical segments,
each marked with a different prize. Seven of the segments are
labeled "Free Entree" or "Free Appetizer." The other three are
labeled "Free Valet Parking."
Let the digits 0-6 represent winning free food and 7-9 represent
winning valet parking.
Using the line of random numbers, what is the best estimate of the
number of free food prizes won by the next 20 patrons who spin the
wheel? Answer: D. 15
,◉ A study reported that about half of high school seniors study for
upcoming math tests. To find out if this applies to seniors at Garfield
High School, an SRS of 30 seniors was asked if they study for their
math tests. Nineteen responded "Yes."
A dotplot is provided showing the results of 40 trials of this
simulation.
Does this provide convincing evidence that seniors at Garfield High
School study more than the report stated? Answer: C. Yes, only one
trial had a result of 19 or larger.
◉ A contractor claims that she finishes a job on time 90% of the
time. Last month, she only completed 7 out of her 10 jobs on time.
To see if this is surprisingly low, a simulation was conducted 100
times under the assumption that she really does complete 90% of
her jobs on time.
The dotplot contains 100 trials of this simulation.
Based on this dotplot and the sample of last month's on-time
completions, which conclusion can be drawn? Answer: D. The
dotplot does not provide convincing evidence that her true, on-time
completion rate is less than 90% because 7 or fewer on-time
completions happened 19% of the time in the simulation.
,◉ A manufacturer of baseball hats claims that approximately 30% of
people regularly wear baseball hats. From a random sample of 20
students at your school, you find that only four wear baseball hats
regularly. This gives you reason to believe that the manufacturer's
claim of 30% is too high.
Let the digits 0-2 represent wearing a baseball hat (H) and the digits
3-9 represent not wearing a baseball hat (N). Use the table of
random numbers to run one trial of this simulation.
Which is the correct sequence of outcomes? Answer: A. NNNNN
HHNNN NNNHN NHNHN
◉ A teacher claims that there is a 50% chance that she will collect
homework for a grade on any given day. One week, she collected all
five daily homework assignments. A student in this class is upset and
explains that the teacher should not collect any homework
assignments the following week in order to honor her 50%
probability claim.
Is the student's reasoning correct? Answer: D. No, collecting
homework and not collecting homework are equally likely in the
long run, so whether or not the teacher collects homework on any
single day cannot be determined.
◉ Carlos thinks the traffic light to get out of his neighborhood is red
more often than green. He decides to collect data to determine the
probability of the light being red upon his approach. The graph of his
long-run relative frequencies is shown.
, Which conclusion can be drawn from this graph? Answer: B. About
63% of the time, the traffic light is red when Carlos leaves his
neighborhood.
◉ Forty percent of the beads in a bag of more than 10,000 beads are
yellow. Suzy pulls out 10 beads, one at a time with replacement, and
notes that eight of these beads are yellow. She says the next bead
pulled out will not be yellow because a yellow bead has been pulled
out too many times in a row.
Is Suzy's reasoning correct? Answer: D. No, it is true that the
probability of pulling a yellow bead is 0.40, but Suzy should not
expect that exactly 40% of such a small number of beads pulled will
be yellow.
◉ The manufacturer of a soccer ball claims that only 3% of the
soccer balls produced are faulty. An employee of this company
examines the long-run relative frequency of faulty soccer balls
produced as shown in the graph.
Which conclusion can be drawn from this graph? Answer: D. The
graph shows that the probability of producing a faulty soccer ball is
about 0.06; therefore, we should not believe the company's claim
that only 3% of the produced soccer balls are faulty.
