## PEC EPE Exam Probability and Statistical Methods Numerical Questions

Click here for PEC EPE Exam Probability and Statistical Methods MCQs

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**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 = โVariance = โ50 โ 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) โ 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 โค 3) = 1 – (e^-2 * (2^0/0!) + e^-2 * (2^1/1!) + e^-2 * (2^2/2!)) โ 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 โ 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).