College Math Placement Test Statistics 5 — Questions and Answers
Question 1: A data set has mean 50 and standard deviation 10. A value of 70 has a z-score of:
- 1
- 2 (Correct answer)
- −2
- 7
Correct answer: 2
z = (70 − 50) / 10 = 20/10 = 2.
Question 2: If events A and B are independent and P(A) = 0.4, P(B) = 0.5, what is P(A and B)?
- 0.9
- 0.1
- 0.2 (Correct answer)
- 0.45
Correct answer: 0.2
For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.
Question 3: A histogram with bars of roughly equal height suggests the distribution is:
- Normal
- Skewed right
- Bimodal
- Uniform (Correct answer)
Correct answer: Uniform
Equal bar heights indicate that all values occur with similar frequency, which is characteristic of a uniform distribution.
Question 4: The stem-and-leaf plot shows stems 1, 2, 3 with leaves 2 3 | 1 4 6 | 0 5. What is the median?
- 21
- 24 (Correct answer)
- 30
- 26
Correct answer: 24
The values in order are 12, 13, 21, 24, 26, 30, 35; the 4th (middle) value is 24.
Question 5: A confidence interval is reported as (48, 56). What is the margin of error?
- 8
- 4 (Correct answer)
- 52
- 2
Correct answer: 4
The margin of error is half the width of the interval: (56 − 48) / 2 = 4.
Question 6: Which of the following best describes an observational study?
- Researchers assign subjects to treatment and control groups
- Researchers manipulate variables to determine cause and effect
- Researchers collect data without manipulating any variables (Correct answer)
- Researchers use a placebo to control for bias
Correct answer: Researchers collect data without manipulating any variables
In an observational study, researchers observe and record data without intervening or manipulating variables.
Question 7: Which measure best describes the center of a data set that contains an extreme outlier?
- Mean
- Mode
- Median (Correct answer)
- Standard deviation
Correct answer: Median
The median is resistant to outliers because it depends only on the middle value(s), not the magnitude of extreme values.
College Math Placement Test Statistics 5
A data set has mean 50 and standard deviation 10.
A value of 70 has a z-score of: