FAST Probability and Distributions 3 — Questions and Answers
Question 1: In a binomial experiment with n=10 and p=0.3, what is the expected number of successes?
- 3 (Correct answer)
- 7
- 0.3
- 30
Correct answer: 3
The expected value of a binomial distribution is E(X) = n × p = 10 × 0.3 = 3.
Question 2: What does a z-score of 2.0 indicate about a data point?
- It is 2 standard deviations below the mean
- It is twice the mean
- It is 2 standard deviations above the mean (Correct answer)
- It is in the top 2% of values
Correct answer: It is 2 standard deviations above the mean
A z-score of 2.0 means the data point is exactly 2 standard deviations above the mean.
Question 3: Events A and B are independent. P(A) = 0.6 and P(B) = 0.5. What is P(A and B)?
- 1.1
- 0.3 (Correct answer)
- 0.55
- 0.1
Correct answer: 0.3
For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.3.
Question 4: A dataset follows a uniform distribution between 10 and 30. What is the probability that a randomly selected value falls between 15 and 25?
- 1/2 (Correct answer)
- 1/4
- 2/3
- 3/4
Correct answer: 1/2
For a uniform distribution, P(15 ≤ X ≤ 25) = (25−15)/(30−10) = 10/20 = 1/2.
Question 5: A test has 5 multiple-choice questions each with 4 options. If a student guesses randomly, what is the probability of getting all 5 correct?
- 1/20
- 1/1024 (Correct answer)
- 5/4
- 1/625
Correct answer: 1/1024
Each question has a 1/4 chance of being correct, so all 5 correct = (1/4)^5 = 1/1024.
Question 6: Which measure of center is MOST resistant to outliers in a dataset?
- Mean
- Mode
- Median (Correct answer)
- Range
Correct answer: Median
The median is resistant to outliers because it depends only on the middle value, not the magnitude of extreme values.
Question 7: A Poisson distribution with λ=4 models the number of customer arrivals per hour. What is the mean number of arrivals?
- 2
- 4 (Correct answer)
- 16
- 0.25
Correct answer: 4
For a Poisson distribution, the mean equals the parameter λ, which is 4.
FAST Probability and Distributions 3
In a binomial experiment with n=10 and p=0.3, what is the expected number of successes?