1. In a Poisson distribution, if λ=2\lambda = 2λ=2, what is the probability of observing
exactly 3 events?
A. 0.180
B. 0.270
C. 0.135
D. 0.045
Answer: A) 0.180
Rationale: The probability for exactly 3 events is calculated using the Poisson formula
P(X=x)=λxe−λx!P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}P(X=x)=x!λxe−λ,
which results in 0.180.
2. What is the mode of the following distribution: 2, 2, 3, 5, 5, 5, 8, 8, 9?
A. 5
B. 2
C. 3
D. 8
Answer: A) 5
Rationale: The mode is the most frequent number, which is 5 in this dataset.
3. What does a p-value of 0.03 indicate in a hypothesis test?
A. Strong evidence against the null hypothesis
B. Strong evidence in favor of the null hypothesis
C. Weak evidence against the null hypothesis
D. The test is inconclusive
Answer: A) Strong evidence against the null hypothesis
Rationale: A p-value of 0.03 indicates that there is strong evidence against the null
hypothesis at the 5% significance level.
4. In a normal distribution, what percentage of data lies within 1 standard deviation of
the mean?
A. 95%
B. 68%
C. 99.7%
D. 50%
Answer: B) 68%
Rationale: In a normal distribution, approximately 68% of the data lies within 1
standard deviation of the mean.
5. A probability distribution is defined as P(X=x)=0.2P(X = x) = 0.2P(X=x)=0.2 for all
values of xxx from 1 to 5. What type of distribution is this?
A. Binomial distribution
B. Poisson distribution
C. Uniform distribution
D. Normal distribution
Answer: C) Uniform distribution
Rationale: A uniform distribution assigns equal probabilities to all possible outcomes,
which is the case here.
, 6. The probability of success in a binomial distribution is 0.6. What is the probability of
having exactly 3 successes in 5 trials?
A. 0.400
B. 0.250
C. 0.3456
D. 0.512
Answer: A) 0.400
Rationale: Using the binomial probability formula P(X=x)=C(n,x)px(1−p)n−xP(X = x) =
C(n, x) p^x (1-p)^{n-x}P(X=x)=C(n,x)px(1−p)n−x, where n=5n = 5n=5, p=0.6p =
0.6p=0.6, and x=3x = 3x=3, the probability is approximately 0.400.
7. What does a scatterplot with a strong downward slope indicate about the relationship
between two variables?
A. A strong positive linear relationship
B. A weak positive relationship
C. A strong negative linear relationship
D. No relationship
Answer: C) A strong negative linear relationship
Rationale: A downward slope on a scatterplot indicates a negative relationship between
the variables.
8. If a die is rolled twice, what is the probability of getting a sum of 7?
A. 1/6
B. 1/36
C. 5/36
D. 1/9
Answer: C) 5/36
Rationale: The possible combinations that give a sum of 7 are: (1,6), (2,5), (3,4),
(4,3), (5,2), and (6,1). There are 6 possible outcomes, and since the die is rolled twice,
the total number of outcomes is 6×6=366 \times 6 = 366×6=36, so the probability is
536\frac{5}{36}365.
9. 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.
10. 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.
exactly 3 events?
A. 0.180
B. 0.270
C. 0.135
D. 0.045
Answer: A) 0.180
Rationale: The probability for exactly 3 events is calculated using the Poisson formula
P(X=x)=λxe−λx!P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}P(X=x)=x!λxe−λ,
which results in 0.180.
2. What is the mode of the following distribution: 2, 2, 3, 5, 5, 5, 8, 8, 9?
A. 5
B. 2
C. 3
D. 8
Answer: A) 5
Rationale: The mode is the most frequent number, which is 5 in this dataset.
3. What does a p-value of 0.03 indicate in a hypothesis test?
A. Strong evidence against the null hypothesis
B. Strong evidence in favor of the null hypothesis
C. Weak evidence against the null hypothesis
D. The test is inconclusive
Answer: A) Strong evidence against the null hypothesis
Rationale: A p-value of 0.03 indicates that there is strong evidence against the null
hypothesis at the 5% significance level.
4. In a normal distribution, what percentage of data lies within 1 standard deviation of
the mean?
A. 95%
B. 68%
C. 99.7%
D. 50%
Answer: B) 68%
Rationale: In a normal distribution, approximately 68% of the data lies within 1
standard deviation of the mean.
5. A probability distribution is defined as P(X=x)=0.2P(X = x) = 0.2P(X=x)=0.2 for all
values of xxx from 1 to 5. What type of distribution is this?
A. Binomial distribution
B. Poisson distribution
C. Uniform distribution
D. Normal distribution
Answer: C) Uniform distribution
Rationale: A uniform distribution assigns equal probabilities to all possible outcomes,
which is the case here.
, 6. The probability of success in a binomial distribution is 0.6. What is the probability of
having exactly 3 successes in 5 trials?
A. 0.400
B. 0.250
C. 0.3456
D. 0.512
Answer: A) 0.400
Rationale: Using the binomial probability formula P(X=x)=C(n,x)px(1−p)n−xP(X = x) =
C(n, x) p^x (1-p)^{n-x}P(X=x)=C(n,x)px(1−p)n−x, where n=5n = 5n=5, p=0.6p =
0.6p=0.6, and x=3x = 3x=3, the probability is approximately 0.400.
7. What does a scatterplot with a strong downward slope indicate about the relationship
between two variables?
A. A strong positive linear relationship
B. A weak positive relationship
C. A strong negative linear relationship
D. No relationship
Answer: C) A strong negative linear relationship
Rationale: A downward slope on a scatterplot indicates a negative relationship between
the variables.
8. If a die is rolled twice, what is the probability of getting a sum of 7?
A. 1/6
B. 1/36
C. 5/36
D. 1/9
Answer: C) 5/36
Rationale: The possible combinations that give a sum of 7 are: (1,6), (2,5), (3,4),
(4,3), (5,2), and (6,1). There are 6 possible outcomes, and since the die is rolled twice,
the total number of outcomes is 6×6=366 \times 6 = 366×6=36, so the probability is
536\frac{5}{36}365.
9. 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.
10. 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.
