Probability and Statistics Quiz

A researcher wants to model the test scores of students in a large university. The scores are symmetrically distributed with most students scoring near the average. Which distribution is most appropriate for modelling the scores?

• Poisson Distribution

• Exponential Distribution

• Binomial Distribution

• Normal Distribution

In a factory, the heights of employees are normally distributed with a mean of 170 cm and a standard deviation of 10 cm. What is the probability that an employee is taller than 180 cm?

• 0.3413

• 0.0228

• 0.5

• 0.1587

A marketing company conducts a survey where they ask 5 customers if they will buy a new product. If the probability of a customer agreeing is 0.6, what is the probability that exactly 3 customers will agree?

• 0.2765

• 0.3456

• 0.4

• 0.2

In a classroom of 20 students, the probability of each student passing an exam is 0.7. What is the mean number of students expected to pass the exam?

• 7

• 10

• 6

• 14

A factory experiences an average of 3 breakdowns per week. What is the probability that the factory will have exactly 2 breakdowns in a given week?

• 0.1508

• 0.1991

• 0.2241

• 0.1804

The time between customer arrivals at a store is exponentially distributed with a mean time of 5 minutes. What is the probability that the next customer will arrive in less than 3 minutes?

• 0.6321

• 0.4512

• 0.5

• 0.2231

A company conducts a survey on a sample of 100 customers, where the probability of a customer purchasing a product is 0.6. If the sample size is large, what distribution can be used to approximate the binomial distribution?

• Log-Normal Distribution

• Poisson Distribution

• Exponential Distribution

• Normal Distribution

The number of cars passing through a toll booth follows a Poisson distribution with an average of 10 cars per hour. What is the probability that 15 cars will pass through in one hour?

• 0.0231

• 0.0347

• 0.0419

• 0.0320

A researcher is studying the time it takes for a computer to process a task. If the processing times are exponentially distributed with a mean of 4 seconds, what is the probability that a task will be completed in less than 2 seconds?

• 0.2231

• 0.1813

• 0.6321

• 0.3935

A school has a class of 30 students, and the probability of a student being absent on a given day is 0.2. What is the probability that exactly 5 students will be absent?

• 0.2150

• 0.2500

• 0.1855

• 0.2023