CAA Probability & Statistics — Questions and Answers
Question 1: What is the probability of rolling a sum of 7 with two six-sided dice?
- 1/12
- 1/6 (Correct answer)
- 1/8
- 1/4
Correct answer: 1/6
There are six possible outcomes that result in a sum of 7 out of 36 total outcomes, giving a probability of 6/36 = 1/6.
Question 2: What does the expected value of a probability distribution represent?
- The most frequently occurring value
- The long-term average outcome (Correct answer)
- The range of values
- The highest probability outcome
Correct answer: The long-term average outcome
The expected value represents the long-term average outcome of a random variable if the experiment is repeated many times.
Question 3: If a fair coin is flipped twice, what is the probability of getting two heads?
- 1/4 (Correct answer)
- 1/2
- 1/3
- 1/8
Correct answer: 1/4
Each flip has a probability of 1/2 for heads. The probability of two heads is (1/2) × (1/2) = 1/4.
Question 4: Which measure of central tendency is most affected by extreme values?
- Median
- Mean (Correct answer)
- Mode
- Range
Correct answer: Mean
The mean is most affected by extreme values because it considers all values in a dataset, including outliers.
Question 5: What does a standard deviation measure in a dataset?
- The difference between highest and lowest values
- The spread of values around the mean (Correct answer)
- The middle value in the dataset
- The most frequently occurring value
Correct answer: The spread of values around the mean
The standard deviation measures the spread of data values from the mean, indicating variability within the dataset.
Question 6: In a normal distribution, what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 75%
- 95%
Correct answer: 68%
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
CAA Probability & Statistics
What is the probability of rolling a sum of 7 with two six-sided dice?