ISAT Probability and Statistical Analysis 2 — Questions and Answers
Question 1: A bag contains 4 red, 3 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability both are green?
- 5/33 (Correct answer)
- 25/144
- 5/22
- 10/132
Correct answer: 5/33
P(both green) = (5/12) × (4/11) = 20/132 = 5/33.
Question 2: The median of a data set is best described as:
- The value that appears most often
- The arithmetic average of all values
- The middle value when data is ordered (Correct answer)
- Half the range of the data
Correct answer: The middle value when data is ordered
The median is the middle value of an ordered dataset, or the average of the two middle values when the count is even.
Question 3: Events A and B are mutually exclusive. P(A) = 0.35 and P(B) = 0.45. What is P(A or B)?
- 0.1575
- 0.8 (Correct answer)
- 0.65
- 0.55
Correct answer: 0.8
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.35 + 0.45 = 0.80.
Question 4: A dataset has values: 2, 4, 4, 6, 8, 10. What is the variance?
- 6.33 (Correct answer)
- 7.0
- 8.0
- 5.67
Correct answer: 6.33
Mean = 34/6 ≈ 5.67; variance = [(3.67²+1.67²+1.67²+0.11²+5.45²+19.0²)/6] ≈ 6.33 (population variance).
Question 5: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical rule states that about 68% of data lies within ±1 standard deviation of the mean in a normal distribution.
Question 6: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
- 1/4
- 3/8
- 1/2
- 1/4 (Correct answer)
Correct answer: 1/4
C(4,3) × (1/2)³ × (1/2)¹ = 4 × (1/16) = 4/16 = 1/4.
Question 7: Which measure of central tendency is most affected by extreme outliers?
- Median
- Mode
- Mean (Correct answer)
- Midrange
Correct answer: Mean
The mean is calculated using all values, so a single extreme outlier can pull it significantly away from the center of the data.
ISAT Probability and Statistical Analysis 2
A bag contains 4 red, 3 blue, and 5 green marbles.
If two marbles are drawn without replacement, what is the probability both are green?