PEC EPE Exam Probability and Statistical Methods Numerical Questions

PEC EPE Exam Probability and Statistical Methods Numerical Questions

Click here for PEC EPE Exam Probability and Statistical Methods MCQs

Other PEC EPE Exam Past Paper Questions

A fair six-sided die is rolled. What is the probability of rolling a 3 or a 5?

Solution: Probability = P(3) + P(5) = 1/6 + 1/6 = 1/3.

Calculate the mean of the dataset: [10, 15, 20, 25, 30].

Solution: Mean = (10 + 15 + 20 + 25 + 30) / 5 = 20.

A dataset has a standard deviation of 4 and a mean of 50. Calculate the coefficient of variation.

Solution: Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4 / 50) * 100 = 8%.

A construction project has a 15% chance of being delayed due to weather. If there are 10 independent projects, what is the probability that exactly 2 will be delayed?

Solution: Probability = (10C2) * (0.15^2) * (0.85^8).

The heights (in cm) of a group of students are: [160, 165, 170, 175, 180]. Calculate the mean and standard deviation.

Solution: Mean = (160 + 165 + 170 + 175 + 180) / 5 = 170.

Calculate variance: [(160 – 170)^2 + (165 – 170)^2 + (170 – 170)^2 + (175 – 170)^2 + (180 – 170)^2] / 5 = 50.

Standard Deviation = √Variance = √50 ≈ 7.07.

The time it takes for a civil engineer to complete a task follows an exponential distribution with a mean of 6 hours. What is the probability that the task is completed in less than 4 hours?

Solution: Using exponential distribution formula: P(X < 4) = 1 – e^(-4/6) ≈ 0.4866.

In a survey, 60% of civil engineering students use software for project management. If 5 students are randomly selected, what is the probability that exactly 3 of them use project management software?

Solution: Probability = (5C3) * (0.60^3) * (0.40^2).

The number of accidents at a construction site follows a Poisson distribution with an average of 2 accidents per week. Calculate the probability of having more than 3 accidents in a week.

Solution: Using Poisson distribution formula: P(X > 3) = 1 – P(X ≤ 3) = 1 – (e^-2 * (2^0/0!) + e^-2 * (2^1/1!) + e^-2 * (2^2/2!)) ≈ 0.5768.

The diameters of bolts used in a construction project follow a normal distribution with a mean of 12 mm and a standard deviation of 0.5 mm. What percentage of bolts will have a diameter between 11.5 mm and 12.5 mm?

Solution: Z-score for 11.5 mm = (11.5 – 12) / 0.5 = -1.

Z-score for 12.5 mm = (12.5 – 12) / 0.5 = 1.

Area between -1 and 1 under the standard normal curve ≈ 0.6826, or 68.26%.

A civil engineering company employs 200 engineers, 25% of whom are female. If 20 engineers are randomly selected, what is the probability that exactly 5 of them are female?

Solution: Probability = (20C5) * (0.25^5) * (0.75^15).