STAT Scientific and Mathematical Reasoning 3 — Questions and Answers
Question 1: A data set of exam scores has a mean of 70 and a standard deviation of 10. If a student scores 90, how many standard deviations above the mean is this score?
- 1
- 1.5
- 2 (Correct answer)
- 2.5
Correct answer: 2
z = (90 − 70) ÷ 10 = 2, so the score is exactly 2 standard deviations above the mean.
Question 2: When a solid is heated at constant pressure, which energy change primarily occurs at its melting point?
- Kinetic energy of particles increases rapidly
- Potential energy of particles increases while temperature stays constant (Correct answer)
- Both kinetic and potential energy decrease
- Temperature rises sharply while potential energy stays constant
Correct answer: Potential energy of particles increases while temperature stays constant
At the melting point, energy input overcomes intermolecular forces (increases potential energy) without raising temperature.
Question 3: A rectangle has a length that is three times its width. If the area is 75 cm², what is the width?
- 3 cm
- 5 cm (Correct answer)
- 7.5 cm
- 15 cm
Correct answer: 5 cm
Let width = w; then 3w × w = 75, so 3w² = 75, w² = 25, w = 5 cm.
Question 4: A scientist observes that taller plants produce more seeds. She concludes that height causes increased seed production. What is the main flaw in this reasoning?
- She did not measure plant height accurately
- Correlation does not imply causation — a third factor may explain both (Correct answer)
- She should have used a larger ruler
- Only experimental plants can be studied for seed production
Correct answer: Correlation does not imply causation — a third factor may explain both
An observed correlation between two variables cannot establish causality without ruling out confounding factors.
Question 5: Light travels from water (refractive index 1.33) into air (refractive index 1.00). Compared to its speed in water, the speed of light in air is:
- Slower
- The same
- Faster (Correct answer)
- Cannot be determined without the angle of incidence
Correct answer: Faster
Refractive index = c/v; a lower refractive index means higher speed, so light travels faster in air than in water.
Question 6: A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
- 4/25
- 2/15 (Correct answer)
- 1/5
- 4/10
Correct answer: 2/15
P(both red) = (4/10) × (3/9) = 12/90 = 2/15.
Question 7: A bar chart shows five cities' average annual rainfall. City C's bar is twice the height of City A's bar. Which conclusion is valid?
- City C receives twice the rainfall of City A (Correct answer)
- City C's climate is twice as wet as City A's overall
- City C has twice as many rainy days as City A
- City C's temperature is lower than City A's
Correct answer: City C receives twice the rainfall of City A
Bar height directly represents the measured value, so twice the bar height means twice the average annual rainfall.
STAT Scientific and Mathematical Reasoning 3
A data set of exam scores has a mean of 70 and a standard deviation of 10.
If a student scores 90, how many standard deviations above the mean is this score?