MATH 225N WEEK 3: STATISTICAL
REASONING - PROBABILITY AND
DISTRIBUTIONS ASSESSMENT
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. Which of the following defines two events as being mutually exclusive?
A. The probability of one event occurring is not affected by the occurrence of the other.
B. The occurrence of one event depends entirely on the outcome of the first event.
C. The sum of their individual probabilities must equal exactly 1.0.
D. The events cannot occur at the same time, meaning their intersection is an empty set.
Answer: D
Conceptual Explanation: Mutually exclusive events are events that cannot happen
simultaneously; if one occurs, the other cannot.
2. In a binomial distribution, what does the variable ‘n’ represent?
A. The probability of success in a single trial.
B. The fixed number of independent trials performed.
C. The number of successful outcomes desired.
D. The standard deviation of the population distribution.
,Answer: B
Conceptual Explanation: In binomial notation, ‘n’ refers to the fixed number of trials in
the experiment.
3. If the probability of an event P(A) is 0.25, what is the probability of its complement, P(A’)?
A. 0.25
B. 0.75
C. 0.50
D. 1.25
Answer: B
Conceptual Explanation: The probability of a complement is calculated as 1 minus the
probability of the event (1 - 0.25 = 0.75).
4. According to the Central Limit Theorem, as the sample size increases, the sampling
distribution of the mean approaches which shape?
A. Uniform Distribution
B. Skewed Left Distribution
C. Bimodal Distribution
D. Normal Distribution
Answer: D
, Conceptual Explanation: The Central Limit Theorem states that regardless of the
population’s distribution, the sampling distribution of the mean will become normal as the
sample size ‘n’ increases (typically n >= 30).
5. What is the primary characteristic of a Standard Normal Distribution?
A. Mean = 1, Standard Deviation = 0
B. Mean = Median = Mode = 100
C. Mean = 0, Standard Deviation = 1
D. A total area under the curve equal to 0.5
Answer: C
Conceptual Explanation: The Standard Normal Distribution is a normal distribution with
a mean of 0 and a standard deviation of 1.
6. Calculate the Z-score for a value of 85, given a population mean of 70 and a standard
deviation of 5.
A. Z = 2.0
B. Z = 3.0
C. Z = 15.0
D. Z = 1.5
Answer: B
Conceptual Explanation: Z = (x - mean) / SD. (85 - 70) / 5 = = 3.0.
REASONING - PROBABILITY AND
DISTRIBUTIONS ASSESSMENT
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. Which of the following defines two events as being mutually exclusive?
A. The probability of one event occurring is not affected by the occurrence of the other.
B. The occurrence of one event depends entirely on the outcome of the first event.
C. The sum of their individual probabilities must equal exactly 1.0.
D. The events cannot occur at the same time, meaning their intersection is an empty set.
Answer: D
Conceptual Explanation: Mutually exclusive events are events that cannot happen
simultaneously; if one occurs, the other cannot.
2. In a binomial distribution, what does the variable ‘n’ represent?
A. The probability of success in a single trial.
B. The fixed number of independent trials performed.
C. The number of successful outcomes desired.
D. The standard deviation of the population distribution.
,Answer: B
Conceptual Explanation: In binomial notation, ‘n’ refers to the fixed number of trials in
the experiment.
3. If the probability of an event P(A) is 0.25, what is the probability of its complement, P(A’)?
A. 0.25
B. 0.75
C. 0.50
D. 1.25
Answer: B
Conceptual Explanation: The probability of a complement is calculated as 1 minus the
probability of the event (1 - 0.25 = 0.75).
4. According to the Central Limit Theorem, as the sample size increases, the sampling
distribution of the mean approaches which shape?
A. Uniform Distribution
B. Skewed Left Distribution
C. Bimodal Distribution
D. Normal Distribution
Answer: D
, Conceptual Explanation: The Central Limit Theorem states that regardless of the
population’s distribution, the sampling distribution of the mean will become normal as the
sample size ‘n’ increases (typically n >= 30).
5. What is the primary characteristic of a Standard Normal Distribution?
A. Mean = 1, Standard Deviation = 0
B. Mean = Median = Mode = 100
C. Mean = 0, Standard Deviation = 1
D. A total area under the curve equal to 0.5
Answer: C
Conceptual Explanation: The Standard Normal Distribution is a normal distribution with
a mean of 0 and a standard deviation of 1.
6. Calculate the Z-score for a value of 85, given a population mean of 70 and a standard
deviation of 5.
A. Z = 2.0
B. Z = 3.0
C. Z = 15.0
D. Z = 1.5
Answer: B
Conceptual Explanation: Z = (x - mean) / SD. (85 - 70) / 5 = = 3.0.
