SOPHIA STATISTICS UNIT 2 MILESTONE
COMPREHENSIVE EXAM 2026 STUDY GUIDE
SOLVED QUESTIONS
◉ Claire wants to determine how her math score, 690, on a
standardized college entrance exam compares to her mother's score,
680, when she took the exam 20 years earlier. The year Claire took
the exam, the mean math score was 510 with a standard deviation of
110 points. When Claire's mother took the exam, the mean math
score was 490 with a standard deviation of 100 points. Who had the
better relative performance? Answer: B. Claire's mother did better
because her z-score is greater than Claire's.
◉ 2-2 Uniform Density Curves Answer:
◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost more than $4.00? Answer: C. 2/3
◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost less than $5.50? Answer: D. 0.833
,◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost between $3.50 and $4.00?? Answer:
C. 1/6
◉ What would the height need to be for this curve to be a density
curve? Answer: B. 1/6
◉ Records show that Oliver is typically 10-30 minutes late for his
shift at work. The distribution for the minutes he is late forms a
consistent pattern, which can be graphed as the given uniform
density curve.
John and Oliver are working a shift that starts at the same time. John
always arrives 8 minutes late. What percentage of the time does
Oliver arrive within 10 minutes of John's arrival time? Answer: C.
40%
◉ Consider the given density curve. What is the value of the median?
A. -10
B. -7
C. -6
D. -2 Answer: C. -6
, ◉ Consider the given uniform density curve. What is the value of the
mean?
A. 4.25
B. 4.5
C. 4.75
D. 5 Answer: B. 4.5
◉ Consider the given density curve. Suppose that the mean value is
10. What is the best approximation for the median?
A. 9
B. 9.5
C. 10
D. 11 Answer: C. 10
◉ Consider the given density curve. What is the value of the median?
A. 3
B. 4
C. 4.5
D. 6 Answer: C. 4.5
COMPREHENSIVE EXAM 2026 STUDY GUIDE
SOLVED QUESTIONS
◉ Claire wants to determine how her math score, 690, on a
standardized college entrance exam compares to her mother's score,
680, when she took the exam 20 years earlier. The year Claire took
the exam, the mean math score was 510 with a standard deviation of
110 points. When Claire's mother took the exam, the mean math
score was 490 with a standard deviation of 100 points. Who had the
better relative performance? Answer: B. Claire's mother did better
because her z-score is greater than Claire's.
◉ 2-2 Uniform Density Curves Answer:
◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost more than $4.00? Answer: C. 2/3
◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost less than $5.50? Answer: D. 0.833
,◉ Data collected from a coffee shop indicate that the price of a drink
forms a consistent pattern that can be graphed as the given uniform
density curve.
What proportion of drinks cost between $3.50 and $4.00?? Answer:
C. 1/6
◉ What would the height need to be for this curve to be a density
curve? Answer: B. 1/6
◉ Records show that Oliver is typically 10-30 minutes late for his
shift at work. The distribution for the minutes he is late forms a
consistent pattern, which can be graphed as the given uniform
density curve.
John and Oliver are working a shift that starts at the same time. John
always arrives 8 minutes late. What percentage of the time does
Oliver arrive within 10 minutes of John's arrival time? Answer: C.
40%
◉ Consider the given density curve. What is the value of the median?
A. -10
B. -7
C. -6
D. -2 Answer: C. -6
, ◉ Consider the given uniform density curve. What is the value of the
mean?
A. 4.25
B. 4.5
C. 4.75
D. 5 Answer: B. 4.5
◉ Consider the given density curve. Suppose that the mean value is
10. What is the best approximation for the median?
A. 9
B. 9.5
C. 10
D. 11 Answer: C. 10
◉ Consider the given density curve. What is the value of the median?
A. 3
B. 4
C. 4.5
D. 6 Answer: C. 4.5
