STAT 200 WEEK 3: ADVANCED
PROBABILITY AND DISTRIBUTIONS
QUESTIONS AND ANSWERS
1. If events A and B are independent, which of the following statements must be true?
A. P(A and B) = P(A) + P(B)
B. P(A and B) = 0
C. P(A | B) = P(A)
D. P(A or B) = P(A) * P(B)
Answer: C
Conceptual Explanation: Independence by definition means that the occurrence of one
event does not change the probability of the other; thus, P(A | B) = P(A).
2. A discrete random variable X has a probability distribution where P(X=1)=0.2, P(X=2)=0.5,
and P(X=3)=0.3. What is the expected value E(X)?
A. 2.0
B. 1.8
C. 2.5
,D. 2.1
Answer: D
Conceptual Explanation: E(X) = (10.2) + (20.5) + (3*0.3) = 0.2 + 1.0 + 0.9 = 2.1.
3. In a binomial distribution with n = 10 and p = 0.4, what is the mean (expected value)?
A. 4.0
B. 6.0
C. 2.4
D. 5.0
Answer: A
Conceptual Explanation: The mean of a binomial distribution is calculated as mu = n *
p. Here, 10 * 0.4 = 4.0.
4. Which of the following is a requirement for a distribution to be a binomial distribution?
A. The probability of success remains constant for each trial.
B. There are at least three possible outcomes for each trial.
C. The trials are dependent on each other.
D. The number of trials is variable.
Answer: A
, Conceptual Explanation: A binomial distribution requires a fixed number of independent
trials, exactly two outcomes, and a constant probability of success.
5. A standard normal distribution has a mean and standard deviation of:
A. Mean = 1, SD = 0
B. Mean = 1, SD = 1
C. Mean = 0, SD = 1
D. Mean = 0, SD = 0
Answer: C
Conceptual Explanation: By definition, the standard normal distribution (Z-distribution)
is centered at 0 with a spread of 1.
6. Find the z-score for a value of 85 if the population mean is 70 and the standard deviation is
10.
A. 1.5
B. -1.5
C. 15
D. 0.85
Answer: A
Conceptual Explanation: Z = (X - mu) / sigma = (85 - 70) / 10 = = 1.5.
PROBABILITY AND DISTRIBUTIONS
QUESTIONS AND ANSWERS
1. If events A and B are independent, which of the following statements must be true?
A. P(A and B) = P(A) + P(B)
B. P(A and B) = 0
C. P(A | B) = P(A)
D. P(A or B) = P(A) * P(B)
Answer: C
Conceptual Explanation: Independence by definition means that the occurrence of one
event does not change the probability of the other; thus, P(A | B) = P(A).
2. A discrete random variable X has a probability distribution where P(X=1)=0.2, P(X=2)=0.5,
and P(X=3)=0.3. What is the expected value E(X)?
A. 2.0
B. 1.8
C. 2.5
,D. 2.1
Answer: D
Conceptual Explanation: E(X) = (10.2) + (20.5) + (3*0.3) = 0.2 + 1.0 + 0.9 = 2.1.
3. In a binomial distribution with n = 10 and p = 0.4, what is the mean (expected value)?
A. 4.0
B. 6.0
C. 2.4
D. 5.0
Answer: A
Conceptual Explanation: The mean of a binomial distribution is calculated as mu = n *
p. Here, 10 * 0.4 = 4.0.
4. Which of the following is a requirement for a distribution to be a binomial distribution?
A. The probability of success remains constant for each trial.
B. There are at least three possible outcomes for each trial.
C. The trials are dependent on each other.
D. The number of trials is variable.
Answer: A
, Conceptual Explanation: A binomial distribution requires a fixed number of independent
trials, exactly two outcomes, and a constant probability of success.
5. A standard normal distribution has a mean and standard deviation of:
A. Mean = 1, SD = 0
B. Mean = 1, SD = 1
C. Mean = 0, SD = 1
D. Mean = 0, SD = 0
Answer: C
Conceptual Explanation: By definition, the standard normal distribution (Z-distribution)
is centered at 0 with a spread of 1.
6. Find the z-score for a value of 85 if the population mean is 70 and the standard deviation is
10.
A. 1.5
B. -1.5
C. 15
D. 0.85
Answer: A
Conceptual Explanation: Z = (X - mu) / sigma = (85 - 70) / 10 = = 1.5.
