## PEC EPE Exam Probability and Statistical Methods MCQ Questions

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The sample space refers to:

a) A set of experimental outcomes

b) The most probable outcome

c) The average outcome

d) The maximum outcome

Answer: a) A set of experimental outcomes

What is the probability of getting tails when flipping a fair coin?

a) 0.25

b) 0.5

c) 0.75

d) 1.0

Answer: b) 0.5

The average of a dataset is also known as:

a) Median

b) Mode

c) Mean

d) Variance

Answer: c) Mean

The range of a dataset is calculated as:

a) Maximum value – Minimum value

b) Mean + Median

c) Median – Mode

d) Variance / Standard Deviation

Answer: a) Maximum value – Minimum value

If two events are mutually exclusive, what is the probability of both occurring?

a) 0

b) 0.25

c) 0.5

d) 1.0

Answer: a) 0

In a normal distribution, what percentage of data lies within one standard deviation from the mean?

a) 25%

b) 50%

c) 68%

d) 95%

Answer: c) 68%

The Poisson distribution is used for:

a) Continuous data

b) Binary data

c) Counting events over time or space

d) Normally distributed data

Answer: c) Counting events over time or space

The coefficient of variation is a measure of:

a) Spread of data relative to the mean

b) Number of data points

c) Skewness of data

d) Range of data

Answer: a) Spread of data relative to the mean

Which measure of central tendency is sensitive to outliers?

a) Mean

b) Median

c) Mode

d) Standard Deviation

Answer: a) Mean

A construction project has a 15% chance of being delayed due to weather. What is the probability that none of the next 5 projects will be delayed?

a) 0.4437

b) 0.5788

c) 0.7594

d) 0.8681

Answer: a) 0.4437

The standard deviation is the square root of:

a) Mean

b) Variance

c) Median

d) Mode

Answer: b) Variance

Which distribution is used to model the number of successes in a fixed number of independent Bernoulli trials?

a) Normal distribution

b) Poisson distribution

c) Binomial distribution

d) Exponential distribution

Answer: c) Binomial distribution

If events A and B are independent, what is the probability of both A and B occurring?

a) P(A) + P(B)

b) P(A) – P(B)

c) P(A) * P(B)

d) P(A) / P(B)

Answer: c) P(A) * P(B)

The mean of a dataset is 25 and the standard deviation is 4. What is the coefficient of variation?

a) 0.16

b) 0.20

c) 0.64

d) 0.80

Answer: b) 0.20

In a continuous uniform distribution, the probability density function is:

a) U-shaped

b) A straight line

c) Exponential

d) Skewed

Answer: b) A straight line

A civil engineering company employs 80 engineers, 40% of whom are female. If 10 engineers are randomly selected, what is the probability that exactly 4 of them are female?

a) 0.1029

b) 0.2503

c) 0.3569

d) 0.4421

Answer: a) 0.1029

The heights (in cm) of a group of civil engineering students are normally distributed with a mean of 170 cm and a standard deviation of 6 cm. What is the probability that a randomly selected student is between 160 cm and 180 cm tall?

a) 0.1587

b) 0.3413

c) 0.4772

d) 0.6131

Answer: c) 0.4772

The mode of a dataset is:

a) The most frequent value

b) The middle value

c) The average value

d) The smallest value

Answer: a) The most frequent value

The exponential distribution is often used to model:

a) The time between rare events

b) The height of individuals

c) The number of successes in a fixed number of trials

d) Continuous data with no upper limit

Answer: a) The time between rare events

The sum of probabilities of all possible outcomes in a sample space is equal to:

a) 0

b) 0.5

c) 1

d) 2

Answer: c) 1