1. 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.
2. 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).
3. A sample of 50 students has a mean score of 70 and a standard deviation of 10.
What is the standard error of the mean?
A. 1.41
B. 2.00
C. 0.50
D. 0.20
Answer: A) 1.41
Rationale: Standard error = σ / √n = 10 / √50 ≈ 1.41.
4. What does the term "sampling error" refer to?
A. The error in data collection
B. The difference between a sample statistic and the population parameter
C. The error caused by human bias
D. The discrepancy between actual and theoretical probabilities
Answer: B) The difference between a sample statistic and the population parameter
Rationale: Sampling error refers to the natural variability that occurs when taking a
sample from a population, causing the sample statistic to differ from the true
population parameter.
5. What is the formula for the standard deviation of a binomial distribution?
A. np(1−p)\sqrt{np(1-p)}np(1−p)
B. n(1−p)\sqrt{n(1-p)}n(1−p)
C. p(1−p)\sqrt{p(1-p)}p(1−p)
D. npnpnp
Answer: A) np(1−p)\sqrt{np(1-p)}np(1−p)
Rationale: The standard deviation of a binomial distribution is np(1−p)\sqrt{np(1-
p)}np(1−p), where nnn is the number of trials and ppp is the probability of success.
, 6. In a regression analysis, what does the coefficient of determination (R²) measure?
A. The strength and direction of the linear relationship
B. The proportion of the variance in the dependent variable that is explained by the
independent variable
C. The slope of the regression line
D. The y-intercept of the regression line
Answer: B) The proportion of the variance in the dependent variable that is explained
by the independent variable
Rationale: R² measures how well the regression model explains the variation in the
dependent variable.
7. 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.
8. 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.
9. The data set consists of the values: 3, 4, 6, 7, 9. What is the range?
A. 6
B. 5
C. 4
D. 3
Answer: B) 6
Rationale: The range is the difference between the maximum and minimum values:
9−3=69 - 3 = 69−3=6.
10. What is the variance of the following data: 2, 4, 6, 8, 10?
A. 8
B. 12
C. 15
D. 10
Answer: A) 8
Rationale: The variance is calculated as 1n∑(xi−xˉ)2\frac{1}{n} \sum (x_i -
\bar{x})^2n1∑(xi−xˉ)2. For this data, the variance is 8.
11. What does a scatterplot with a strong downward slope indicate about the
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.
2. 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).
3. A sample of 50 students has a mean score of 70 and a standard deviation of 10.
What is the standard error of the mean?
A. 1.41
B. 2.00
C. 0.50
D. 0.20
Answer: A) 1.41
Rationale: Standard error = σ / √n = 10 / √50 ≈ 1.41.
4. What does the term "sampling error" refer to?
A. The error in data collection
B. The difference between a sample statistic and the population parameter
C. The error caused by human bias
D. The discrepancy between actual and theoretical probabilities
Answer: B) The difference between a sample statistic and the population parameter
Rationale: Sampling error refers to the natural variability that occurs when taking a
sample from a population, causing the sample statistic to differ from the true
population parameter.
5. What is the formula for the standard deviation of a binomial distribution?
A. np(1−p)\sqrt{np(1-p)}np(1−p)
B. n(1−p)\sqrt{n(1-p)}n(1−p)
C. p(1−p)\sqrt{p(1-p)}p(1−p)
D. npnpnp
Answer: A) np(1−p)\sqrt{np(1-p)}np(1−p)
Rationale: The standard deviation of a binomial distribution is np(1−p)\sqrt{np(1-
p)}np(1−p), where nnn is the number of trials and ppp is the probability of success.
, 6. In a regression analysis, what does the coefficient of determination (R²) measure?
A. The strength and direction of the linear relationship
B. The proportion of the variance in the dependent variable that is explained by the
independent variable
C. The slope of the regression line
D. The y-intercept of the regression line
Answer: B) The proportion of the variance in the dependent variable that is explained
by the independent variable
Rationale: R² measures how well the regression model explains the variation in the
dependent variable.
7. 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.
8. 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.
9. The data set consists of the values: 3, 4, 6, 7, 9. What is the range?
A. 6
B. 5
C. 4
D. 3
Answer: B) 6
Rationale: The range is the difference between the maximum and minimum values:
9−3=69 - 3 = 69−3=6.
10. What is the variance of the following data: 2, 4, 6, 8, 10?
A. 8
B. 12
C. 15
D. 10
Answer: A) 8
Rationale: The variance is calculated as 1n∑(xi−xˉ)2\frac{1}{n} \sum (x_i -
\bar{x})^2n1∑(xi−xˉ)2. For this data, the variance is 8.
11. What does a scatterplot with a strong downward slope indicate about the
