1. A student scores 75 in a test where the mean score is 60 and the standard deviation
is 5. What is the student's z-score?
A. 3
B. 2.5
C. 2
D. 1.5
Answer: A) 3
Rationale: Z-score = X−μσ=75−605=3\frac{X - \mu}{\sigma} = \frac{75 - 60}{5} =
3σX−μ=575−60=3.
2. If the probability of an event occurring is 0.3, what is the probability of the event not
occurring?
A. 0.7
B. 0.3
C. 1.3
D. 0.5
Answer: A) 0.7
Rationale: The probability of the event not occurring is 1 - P(event) = 1 - 0.3 = 0.7.
3. What is the formula for the standard error of the mean?
A. σn\frac{\sigma}{\sqrt{n}}nσ
B. nσ\frac{n}{\sqrt{\sigma}}σn
C. μn\frac{\mu}{\sqrt{n}}nμ
D. 1n\frac{1}{n}n1
Answer: A) σn\frac{\sigma}{\sqrt{n}}nσ
Rationale: The standard error of the mean is σn\frac{\sigma}{\sqrt{n}}nσ, where
σ\sigmaσ is the population standard deviation and nnn is the sample size.
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. 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).
6. 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.
7. 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.
8. 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.
9. The value of a statistic is normally distributed with mean 10 and standard deviation
3. What is the z-score corresponding to the value 13?
A. 1
B. 0.5
C. 0.33
D. 2.5
Answer: A) 1
Rationale: Z-score = X−μσ=13−103=1\frac{X - \mu}{\sigma} = \frac{13 - 10}{3} =
1σX−μ=313−10=1.
10. The value of the coefficient of determination (R²) is 0.81. What does this tell us
about the regression model?
A. 81% of the variation in the dependent variable is explained by the independent
variable.
B. The regression model is not statistically significant.
C. 81% of the variation is due to other factors.
D. The regression model is perfect.
Answer: A) 81% of the variation in the dependent variable is explained by the
independent variable.
Rationale: The coefficient of determination (R²) indicates how much of the variation in
the dependent variable is explained by the independent variable(s).
11. What is the mean of the following data set: 1, 2, 2, 4, 5?
is 5. What is the student's z-score?
A. 3
B. 2.5
C. 2
D. 1.5
Answer: A) 3
Rationale: Z-score = X−μσ=75−605=3\frac{X - \mu}{\sigma} = \frac{75 - 60}{5} =
3σX−μ=575−60=3.
2. If the probability of an event occurring is 0.3, what is the probability of the event not
occurring?
A. 0.7
B. 0.3
C. 1.3
D. 0.5
Answer: A) 0.7
Rationale: The probability of the event not occurring is 1 - P(event) = 1 - 0.3 = 0.7.
3. What is the formula for the standard error of the mean?
A. σn\frac{\sigma}{\sqrt{n}}nσ
B. nσ\frac{n}{\sqrt{\sigma}}σn
C. μn\frac{\mu}{\sqrt{n}}nμ
D. 1n\frac{1}{n}n1
Answer: A) σn\frac{\sigma}{\sqrt{n}}nσ
Rationale: The standard error of the mean is σn\frac{\sigma}{\sqrt{n}}nσ, where
σ\sigmaσ is the population standard deviation and nnn is the sample size.
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. 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).
6. 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.
7. 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.
8. 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.
9. The value of a statistic is normally distributed with mean 10 and standard deviation
3. What is the z-score corresponding to the value 13?
A. 1
B. 0.5
C. 0.33
D. 2.5
Answer: A) 1
Rationale: Z-score = X−μσ=13−103=1\frac{X - \mu}{\sigma} = \frac{13 - 10}{3} =
1σX−μ=313−10=1.
10. The value of the coefficient of determination (R²) is 0.81. What does this tell us
about the regression model?
A. 81% of the variation in the dependent variable is explained by the independent
variable.
B. The regression model is not statistically significant.
C. 81% of the variation is due to other factors.
D. The regression model is perfect.
Answer: A) 81% of the variation in the dependent variable is explained by the
independent variable.
Rationale: The coefficient of determination (R²) indicates how much of the variation in
the dependent variable is explained by the independent variable(s).
11. What is the mean of the following data set: 1, 2, 2, 4, 5?
