1. What is the mean of the following data: 5, 8, 12, 15, 18?
A. 12
B. 10.5
C. 13.5
D. 11
Answer: B) 10.5
Rationale: Mean = (5 + 8 + 12 + 15 + 18) / 5 = = 10.5.
2. A die is rolled once. What is the probability of rolling an even
number?
A. 1/6
B. 1/2
C. 2/3
D. 1/3
Answer: B) 1/2
Rationale: The even numbers on a die are 2, 4, and 6, so the probability
is 3/6 = 1/2.
3. Which of the following is the correct notation for a binomial
distribution?
A. Binomial(n, p)
B. N(μ, σ)
C. Poisson(λ)
D. U(a, b)
Answer: A) Binomial(n, p)
Rationale: The binomial distribution is denoted as Binomial(n, p),
where n is the number of trials, and p is the probability of success in
each trial.
,4. The variance of a dataset is 25. What is the standard deviation?
A. 5
B. 25
C. 10
D. 100
Answer: A) 5
Rationale: Standard deviation = √(variance) = √25 = 5.
5. If two events A and B are independent, what is the probability of
both events occurring?
A. P(A) + P(B)
B. P(A) × P(B)
C. P(A | B) × P(B)
D. 1 - P(A ∩ B)
Answer: B) P(A) × P(B)
Rationale: For independent events, the probability of both occurring is
the product of their individual probabilities.
6. Which of the following is NOT a property of the normal
distribution?
A. Symmetrical
B. Mean, median, and mode are equal
C. It has a fixed mean of 1
D. It is bell-shaped
Answer: C) It has a fixed mean of 1
Rationale: The normal distribution has any mean and standard
deviation. It is not fixed at a mean of 1.
7. A random variable follows a normal distribution with a mean of 10
and a standard deviation of 2. What is the probability that the random
variable is between 8 and 12?
,A. 0.6826
B. 0.9545
C. 0.3413
D. 0.9974
Answer: A) 0.6826
Rationale: For a normal distribution, approximately 68% of values lie
within one standard deviation of the mean (between 8 and 12).
8. The probability of an event A occurring is 0.7. What is the
probability that event A does not occur?
A. 0.7
B. 0.3
C. 1.7
D. 0.5
Answer: B) 0.3
Rationale: The probability that event A does not occur is 1 - P(A) = 1 -
0.7 = 0.3.
9. If the correlation coefficient between two variables is 0.8, what does
this indicate?
A. A strong positive linear relationship
B. A strong negative linear relationship
C. No linear relationship
D. A weak negative linear relationship
Answer: A) A strong positive linear relationship
Rationale: A correlation coefficient of 0.8 indicates a strong positive
relationship between the variables.
10. A sample consists of the following values: 4, 7, 10, 13, 16. What is
the median of the sample?
A. 7
, B. 10
C. 13
D. 9
Answer: B) 10
Rationale: The median is the middle value when the data is ordered.
Here, the middle value is 10.
11. In a binomial distribution with n = 5 and p = 0.4, what is the
probability of exactly 2 successes?
A. 0.2304
B. 0.4096
C. 0.3072
D. 0.0768
Answer: C) 0.3072
Rationale: The probability for exactly 2 successes is given by P(X = 2)
= C(5,2) × (0.4)^2 × (0.6)^3 ≈ 0.3072.
12. Which of the following is true for a Poisson distribution?
A. It has a fixed mean of 1.
B. It is discrete and models the number of events in a fixed interval.
C. It is always symmetrical.
D. It can only be used for continuous data.
Answer: B) It is discrete and models the number of events in a fixed
interval.
Rationale: The Poisson distribution is used for modeling the number of
events in a fixed interval of time or space.
13. What does the Central Limit Theorem state?
A. The distribution of sample means will be normal for sufficiently
large sample sizes, regardless of the population distribution.
B. The variance of the sample means will decrease as the sample size
A. 12
B. 10.5
C. 13.5
D. 11
Answer: B) 10.5
Rationale: Mean = (5 + 8 + 12 + 15 + 18) / 5 = = 10.5.
2. A die is rolled once. What is the probability of rolling an even
number?
A. 1/6
B. 1/2
C. 2/3
D. 1/3
Answer: B) 1/2
Rationale: The even numbers on a die are 2, 4, and 6, so the probability
is 3/6 = 1/2.
3. Which of the following is the correct notation for a binomial
distribution?
A. Binomial(n, p)
B. N(μ, σ)
C. Poisson(λ)
D. U(a, b)
Answer: A) Binomial(n, p)
Rationale: The binomial distribution is denoted as Binomial(n, p),
where n is the number of trials, and p is the probability of success in
each trial.
,4. The variance of a dataset is 25. What is the standard deviation?
A. 5
B. 25
C. 10
D. 100
Answer: A) 5
Rationale: Standard deviation = √(variance) = √25 = 5.
5. If two events A and B are independent, what is the probability of
both events occurring?
A. P(A) + P(B)
B. P(A) × P(B)
C. P(A | B) × P(B)
D. 1 - P(A ∩ B)
Answer: B) P(A) × P(B)
Rationale: For independent events, the probability of both occurring is
the product of their individual probabilities.
6. Which of the following is NOT a property of the normal
distribution?
A. Symmetrical
B. Mean, median, and mode are equal
C. It has a fixed mean of 1
D. It is bell-shaped
Answer: C) It has a fixed mean of 1
Rationale: The normal distribution has any mean and standard
deviation. It is not fixed at a mean of 1.
7. A random variable follows a normal distribution with a mean of 10
and a standard deviation of 2. What is the probability that the random
variable is between 8 and 12?
,A. 0.6826
B. 0.9545
C. 0.3413
D. 0.9974
Answer: A) 0.6826
Rationale: For a normal distribution, approximately 68% of values lie
within one standard deviation of the mean (between 8 and 12).
8. The probability of an event A occurring is 0.7. What is the
probability that event A does not occur?
A. 0.7
B. 0.3
C. 1.7
D. 0.5
Answer: B) 0.3
Rationale: The probability that event A does not occur is 1 - P(A) = 1 -
0.7 = 0.3.
9. If the correlation coefficient between two variables is 0.8, what does
this indicate?
A. A strong positive linear relationship
B. A strong negative linear relationship
C. No linear relationship
D. A weak negative linear relationship
Answer: A) A strong positive linear relationship
Rationale: A correlation coefficient of 0.8 indicates a strong positive
relationship between the variables.
10. A sample consists of the following values: 4, 7, 10, 13, 16. What is
the median of the sample?
A. 7
, B. 10
C. 13
D. 9
Answer: B) 10
Rationale: The median is the middle value when the data is ordered.
Here, the middle value is 10.
11. In a binomial distribution with n = 5 and p = 0.4, what is the
probability of exactly 2 successes?
A. 0.2304
B. 0.4096
C. 0.3072
D. 0.0768
Answer: C) 0.3072
Rationale: The probability for exactly 2 successes is given by P(X = 2)
= C(5,2) × (0.4)^2 × (0.6)^3 ≈ 0.3072.
12. Which of the following is true for a Poisson distribution?
A. It has a fixed mean of 1.
B. It is discrete and models the number of events in a fixed interval.
C. It is always symmetrical.
D. It can only be used for continuous data.
Answer: B) It is discrete and models the number of events in a fixed
interval.
Rationale: The Poisson distribution is used for modeling the number of
events in a fixed interval of time or space.
13. What does the Central Limit Theorem state?
A. The distribution of sample means will be normal for sufficiently
large sample sizes, regardless of the population distribution.
B. The variance of the sample means will decrease as the sample size
