1. The probability of a certain event occurring is 0.7. What is the
probability of the event not occurring?
A. 0.7
B. 0.3
C. 0.5
D. 0.2
Answer: b) 0.3
Rationale: The probability of an event not occurring is the complement
of the event’s probability. Therefore, P(not
event)=1−P(event)=1−0.7=0.3P(\text{not event}) = 1 -
P(\text{event}) = 1 - 0.7 = 0.3P(not event)=1−P(event)=1−0.7=0.3.
2. A fair die is rolled once. What is the probability of rolling a number
greater than 4?
A. 1/3
B. 1/6
C. 1/2
D. 2/3
Answer: a) 1/3
Rationale: The favorable outcomes for a roll greater than 4 are 5 and 6,
so there are 2 favorable outcomes. The probability is 26=13\frac{2}{6}
= \frac{1}{3}62=31.
3. 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.
4. The mean of a data set is 50, and the standard deviation is 10. What
,is the z-score for a value of 60?
A. 1
B. 0
C. 2
D. -1
Answer: a) 1
Rationale: The formula for the z-score is Z=X−μσZ = \frac{X -
\mu}{\sigma}Z=σX−μ, where XXX is the data point, μ\muμ is the
mean, and σ\sigmaσ is the standard deviation. Here, Z=60−5010=1Z
= \frac{60 - 50}{10} = 1Z=1060−50=1.
5. In a normal distribution, approximately what percentage of data
values lie within one standard deviation of the mean?
A. 68%
B. 95%
C. 99.7%
D. 50%
Answer: a) 68%
Rationale: In a normal distribution, approximately 68% of data values
lie within one standard deviation of the mean.
6. If the variance of a data set is 25, what is the standard deviation?
A. 25
B. 5
C. 20
D. 15
Answer: b) 5
Rationale: The standard deviation is the square root of the variance.
25=5\sqrt{25} = 525=5.
7. Which of the following is an example of a discrete random variable?
A. The time it takes for a car to drive to a destination
B. The height of a person
C. The number of heads in 10 coin flips
D. The temperature of a substance
Answer: c) The number of heads in 10 coin flips
, Rationale: A discrete random variable takes on a countable number of
values, like the number of heads in a fixed number of coin flips.
8. The probability of drawing a red card from a standard deck of 52
cards is:
A. 1/2
B. 1/4
C. 1/13
D. 26/52
Answer: a) 1/2
Rationale: A standard deck has 52 cards, and there are 26 red cards (13
hearts and 13 diamonds). Therefore, the probability is
2652=12\frac{26}{52} = \frac{1}{2}5226=21.
9. A box contains 10 balls: 4 red, 3 blue, and 3 green. What is the
probability of selecting a red ball at random?
A. 1/10
B. 2/5
C. 3/10
D. 4/10
Answer: b) 2/5
Rationale: There are 4 red balls and 10 balls in total. The probability is
410=25\frac{4}{10} = \frac{2}{5}104=52.
10. A coin is flipped 3 times. What is the probability of getting exactly
two heads?
A. 1/8
B. 3/8
C. 1/4
D. 1/2
Answer: b) 3/8
Rationale: The possible outcomes for 3 coin flips are: HHH, HHT,
HTH, HTT, THH, THT, TTH, TTT. There are 3 outcomes with
exactly two heads, so the probability is 38\frac{3}{8}83.
11. Which of the following is the formula for the binomial distribution?
probability of the event not occurring?
A. 0.7
B. 0.3
C. 0.5
D. 0.2
Answer: b) 0.3
Rationale: The probability of an event not occurring is the complement
of the event’s probability. Therefore, P(not
event)=1−P(event)=1−0.7=0.3P(\text{not event}) = 1 -
P(\text{event}) = 1 - 0.7 = 0.3P(not event)=1−P(event)=1−0.7=0.3.
2. A fair die is rolled once. What is the probability of rolling a number
greater than 4?
A. 1/3
B. 1/6
C. 1/2
D. 2/3
Answer: a) 1/3
Rationale: The favorable outcomes for a roll greater than 4 are 5 and 6,
so there are 2 favorable outcomes. The probability is 26=13\frac{2}{6}
= \frac{1}{3}62=31.
3. 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.
4. The mean of a data set is 50, and the standard deviation is 10. What
,is the z-score for a value of 60?
A. 1
B. 0
C. 2
D. -1
Answer: a) 1
Rationale: The formula for the z-score is Z=X−μσZ = \frac{X -
\mu}{\sigma}Z=σX−μ, where XXX is the data point, μ\muμ is the
mean, and σ\sigmaσ is the standard deviation. Here, Z=60−5010=1Z
= \frac{60 - 50}{10} = 1Z=1060−50=1.
5. In a normal distribution, approximately what percentage of data
values lie within one standard deviation of the mean?
A. 68%
B. 95%
C. 99.7%
D. 50%
Answer: a) 68%
Rationale: In a normal distribution, approximately 68% of data values
lie within one standard deviation of the mean.
6. If the variance of a data set is 25, what is the standard deviation?
A. 25
B. 5
C. 20
D. 15
Answer: b) 5
Rationale: The standard deviation is the square root of the variance.
25=5\sqrt{25} = 525=5.
7. Which of the following is an example of a discrete random variable?
A. The time it takes for a car to drive to a destination
B. The height of a person
C. The number of heads in 10 coin flips
D. The temperature of a substance
Answer: c) The number of heads in 10 coin flips
, Rationale: A discrete random variable takes on a countable number of
values, like the number of heads in a fixed number of coin flips.
8. The probability of drawing a red card from a standard deck of 52
cards is:
A. 1/2
B. 1/4
C. 1/13
D. 26/52
Answer: a) 1/2
Rationale: A standard deck has 52 cards, and there are 26 red cards (13
hearts and 13 diamonds). Therefore, the probability is
2652=12\frac{26}{52} = \frac{1}{2}5226=21.
9. A box contains 10 balls: 4 red, 3 blue, and 3 green. What is the
probability of selecting a red ball at random?
A. 1/10
B. 2/5
C. 3/10
D. 4/10
Answer: b) 2/5
Rationale: There are 4 red balls and 10 balls in total. The probability is
410=25\frac{4}{10} = \frac{2}{5}104=52.
10. A coin is flipped 3 times. What is the probability of getting exactly
two heads?
A. 1/8
B. 3/8
C. 1/4
D. 1/2
Answer: b) 3/8
Rationale: The possible outcomes for 3 coin flips are: HHH, HHT,
HTH, HTT, THH, THT, TTH, TTT. There are 3 outcomes with
exactly two heads, so the probability is 38\frac{3}{8}83.
11. Which of the following is the formula for the binomial distribution?
