CHAMBERLAIN COLLEGE OF NURSING
- MATH 225N WEEK 4 ADVANCED
STATISTICS QUESTIONS AND
ANSWERS 100% VERIFIED
1. If events A and B are independent, and P(A) = 0.4 and P(B) = 0.5, what is the probability
that both A and B occur?
A. 0.9
B. 0.1
C. 0.7
D. 0.2
Answer: D
Conceptual Explanation: For independent events, P(A and B) = P(A) * P(B). Thus, 0.4 * 0.5
= 0.2.
2. In a binomial distribution with n = 15 and p = 0.3, what is the probability of exactly 4
successes?
A. 0.1876
B. 0.0897
,C. 0.1268
D. 0.2186
Answer: D
Conceptual Explanation: Using the binomial formula P(X=k) = (n choose k) * p^k * q^(n-
k). For n=15, k=4, p=0.3, the calculation yields approximately 0.2186.
3. Which of the following conditions is NOT required for a binomial experiment?
A. The trials must be independent.
B. There must be at least 30 trials.
C. The probability of success must remain constant.
D. There are only two possible outcomes per trial.
Answer: B
Conceptual Explanation: Binomial experiments require a fixed number of trials, but there
is no minimum requirement of 30 trials; that is a rule of thumb for the Central Limit
Theorem.
4. A normal distribution has a mean of 100 and a standard deviation of 15. What is the Z-
score for a value of 130?
A. 1.5
B. -2.0
C. 2.0
, D. 1.0
Answer: C
Conceptual Explanation: Z = (X - mu) / sigma. Here, (130 - 100) / 15 = = 2.0.
5. The standard error of the mean for a population with standard deviation sigma and sample
size n is calculated as:
A. sigma / n
B. sigma * sqrt(n)
C. sigma / sqrt(n)
D. sigma^2 / n
Answer: C
Conceptual Explanation: The standard error is defined as the population standard
deviation divided by the square root of the sample size.
6. What is the probability of Z being less than -1.96 in a standard normal distribution?
A. 0.0500
B. 0.0250
C. 0.9750
D. 0.0100
Answer: B
- MATH 225N WEEK 4 ADVANCED
STATISTICS QUESTIONS AND
ANSWERS 100% VERIFIED
1. If events A and B are independent, and P(A) = 0.4 and P(B) = 0.5, what is the probability
that both A and B occur?
A. 0.9
B. 0.1
C. 0.7
D. 0.2
Answer: D
Conceptual Explanation: For independent events, P(A and B) = P(A) * P(B). Thus, 0.4 * 0.5
= 0.2.
2. In a binomial distribution with n = 15 and p = 0.3, what is the probability of exactly 4
successes?
A. 0.1876
B. 0.0897
,C. 0.1268
D. 0.2186
Answer: D
Conceptual Explanation: Using the binomial formula P(X=k) = (n choose k) * p^k * q^(n-
k). For n=15, k=4, p=0.3, the calculation yields approximately 0.2186.
3. Which of the following conditions is NOT required for a binomial experiment?
A. The trials must be independent.
B. There must be at least 30 trials.
C. The probability of success must remain constant.
D. There are only two possible outcomes per trial.
Answer: B
Conceptual Explanation: Binomial experiments require a fixed number of trials, but there
is no minimum requirement of 30 trials; that is a rule of thumb for the Central Limit
Theorem.
4. A normal distribution has a mean of 100 and a standard deviation of 15. What is the Z-
score for a value of 130?
A. 1.5
B. -2.0
C. 2.0
, D. 1.0
Answer: C
Conceptual Explanation: Z = (X - mu) / sigma. Here, (130 - 100) / 15 = = 2.0.
5. The standard error of the mean for a population with standard deviation sigma and sample
size n is calculated as:
A. sigma / n
B. sigma * sqrt(n)
C. sigma / sqrt(n)
D. sigma^2 / n
Answer: C
Conceptual Explanation: The standard error is defined as the population standard
deviation divided by the square root of the sample size.
6. What is the probability of Z being less than -1.96 in a standard normal distribution?
A. 0.0500
B. 0.0250
C. 0.9750
D. 0.0100
Answer: B
