1. Which of the following describes the shape of the distribution for a large number of
independent trials of a binomial experiment?
A. Uniform distribution
B. Normal distribution
C. Poisson distribution
D. Exponential distribution
Answer: b) Normal distribution
Rationale: According to the Central Limit Theorem, for a large number of trials, a
binomial distribution approaches a normal distribution.
2. In a normal distribution, what percentage of data values lie between the mean and 2
standard deviations above the mean?
A. 68%
B. 13.5%
C. 95%
D. 99.7%
Answer: b) 13.5%
Rationale: In a normal distribution, approximately 13.5% of the data lies between the
mean and 2 standard deviations above the mean.
3. The mean and standard deviation of a normal distribution are 10 and 2, respectively.
What is the z-score of a value of 12?
A. 1
B. 2
C. 0
D. -1
Answer: a) 1
Rationale: The formula for the z-score is Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ,
where X=12X = 12X=12, μ=10\mu = 10μ=10, and σ=2\sigma = 2σ=2. Therefore,
Z=12−102=1Z = \frac{12 - 10}{2} = 1Z=212−10=1.
4. What is the mean of a Poisson distribution with λ=5\lambda = 5λ=5?
A. 5
B. 10
C. 3
D. 1
Answer: a) 5
Rationale: The mean of a Poisson distribution is equal to λ\lambdaλ. Therefore, the
mean is 5.
5. The value of the correlation coefficient lies between:
A. -1 and 1
B. 0 and 1
C. -1 and 0
D. -∞ and ∞
Answer: a) -1 and 1
Rationale: The correlation coefficient ranges from -1 (perfect negative correlation) to 1
(perfect positive correlation).
, 6. What is the probability of drawing two red cards in a row from a standard deck of 52
cards without replacement?
A. 126\frac{1}{26}261
B. 1352⋅1251\frac{13}{52} \cdot \frac{12}{51}5213⋅5112
C. 152⋅1351\frac{1}{52} \cdot \frac{13}{51}521⋅5113
D. 1352⋅1352\frac{13}{52} \cdot \frac{13}{52}5213⋅5213
Answer: b) 1352⋅1251\frac{13}{52} \cdot \frac{12}{51}5213⋅5112
Rationale: The probability of drawing a red card on the first draw is
2652\frac{26}{52}5226. After drawing one red card, there are 25 red cards left, so the
probability of drawing another red card is 2551\frac{25}{51}5125.
7. A dataset has a mean of 30 and a standard deviation of 5. What is the z-score of the
value 40?
A. 2
B. 1
C. 0
D. 3
Answer: a) 2
Rationale: The z-score is Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ, where X=40X
= 40X=40, μ=30\mu = 30μ=30, and σ=5\sigma = 5σ=5. Therefore, Z=40−305=2Z =
\frac{40 - 30}{5} = 2Z=540−30=2.
8. The Poisson distribution is used to model which type of events?
A. Events with a fixed probability of occurring.
B. Events occurring at fixed intervals with a known mean rate.
C. Events that follow a normal distribution.
D. Events that occur in clusters.
Answer: b) Events occurring at fixed intervals with a known mean rate.
Rationale: The Poisson distribution models the probability of a given number of events
occurring in a fixed interval of time or space, with a known mean rate.
9. Which of the following is NOT a property of the normal distribution?
A. The mean, median, and mode are equal.
B. The distribution is symmetric about the mean.
C. It has two peaks.
D. The tails extend infinitely in both directions.
Answer: c) It has two peaks.
Rationale: A normal distribution has a single peak, at the mean. The other properties
are characteristics of a normal distribution.
10. A survey of 100 students shows that 20 prefer chocolate ice cream. What is the
probability that a randomly selected student prefers chocolate ice cream?
A. 0.20
B. 0.80
C. 0.25
D. 0.30
Answer: a) 0.20
Rationale: The probability is the ratio of students who prefer chocolate ice cream to the
total number of students: 20100=0.20\frac{20}{100} = 0.2010020=0.20.
independent trials of a binomial experiment?
A. Uniform distribution
B. Normal distribution
C. Poisson distribution
D. Exponential distribution
Answer: b) Normal distribution
Rationale: According to the Central Limit Theorem, for a large number of trials, a
binomial distribution approaches a normal distribution.
2. In a normal distribution, what percentage of data values lie between the mean and 2
standard deviations above the mean?
A. 68%
B. 13.5%
C. 95%
D. 99.7%
Answer: b) 13.5%
Rationale: In a normal distribution, approximately 13.5% of the data lies between the
mean and 2 standard deviations above the mean.
3. The mean and standard deviation of a normal distribution are 10 and 2, respectively.
What is the z-score of a value of 12?
A. 1
B. 2
C. 0
D. -1
Answer: a) 1
Rationale: The formula for the z-score is Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ,
where X=12X = 12X=12, μ=10\mu = 10μ=10, and σ=2\sigma = 2σ=2. Therefore,
Z=12−102=1Z = \frac{12 - 10}{2} = 1Z=212−10=1.
4. What is the mean of a Poisson distribution with λ=5\lambda = 5λ=5?
A. 5
B. 10
C. 3
D. 1
Answer: a) 5
Rationale: The mean of a Poisson distribution is equal to λ\lambdaλ. Therefore, the
mean is 5.
5. The value of the correlation coefficient lies between:
A. -1 and 1
B. 0 and 1
C. -1 and 0
D. -∞ and ∞
Answer: a) -1 and 1
Rationale: The correlation coefficient ranges from -1 (perfect negative correlation) to 1
(perfect positive correlation).
, 6. What is the probability of drawing two red cards in a row from a standard deck of 52
cards without replacement?
A. 126\frac{1}{26}261
B. 1352⋅1251\frac{13}{52} \cdot \frac{12}{51}5213⋅5112
C. 152⋅1351\frac{1}{52} \cdot \frac{13}{51}521⋅5113
D. 1352⋅1352\frac{13}{52} \cdot \frac{13}{52}5213⋅5213
Answer: b) 1352⋅1251\frac{13}{52} \cdot \frac{12}{51}5213⋅5112
Rationale: The probability of drawing a red card on the first draw is
2652\frac{26}{52}5226. After drawing one red card, there are 25 red cards left, so the
probability of drawing another red card is 2551\frac{25}{51}5125.
7. A dataset has a mean of 30 and a standard deviation of 5. What is the z-score of the
value 40?
A. 2
B. 1
C. 0
D. 3
Answer: a) 2
Rationale: The z-score is Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ, where X=40X
= 40X=40, μ=30\mu = 30μ=30, and σ=5\sigma = 5σ=5. Therefore, Z=40−305=2Z =
\frac{40 - 30}{5} = 2Z=540−30=2.
8. The Poisson distribution is used to model which type of events?
A. Events with a fixed probability of occurring.
B. Events occurring at fixed intervals with a known mean rate.
C. Events that follow a normal distribution.
D. Events that occur in clusters.
Answer: b) Events occurring at fixed intervals with a known mean rate.
Rationale: The Poisson distribution models the probability of a given number of events
occurring in a fixed interval of time or space, with a known mean rate.
9. Which of the following is NOT a property of the normal distribution?
A. The mean, median, and mode are equal.
B. The distribution is symmetric about the mean.
C. It has two peaks.
D. The tails extend infinitely in both directions.
Answer: c) It has two peaks.
Rationale: A normal distribution has a single peak, at the mean. The other properties
are characteristics of a normal distribution.
10. A survey of 100 students shows that 20 prefer chocolate ice cream. What is the
probability that a randomly selected student prefers chocolate ice cream?
A. 0.20
B. 0.80
C. 0.25
D. 0.30
Answer: a) 0.20
Rationale: The probability is the ratio of students who prefer chocolate ice cream to the
total number of students: 20100=0.20\frac{20}{100} = 0.2010020=0.20.
