5. Statistics

Discrete Distributions — Quiz

Test your understanding of discrete distributions with 5 practice questions.

Practice Questions

Question 1

A random variable $X$ follows a Binomial distribution $B(n, p)$. If the mean of the distribution is $4$ and the variance is $2.4$, what are the values of $n$ and $p$?

Question 2

The number of defects in a manufactured item follows a Poisson distribution with a mean of $0.2$ defects per item. What is the probability that a randomly selected item has at least one defect?

Question 3

A Binomial distribution can be approximated by a Normal distribution when certain conditions are met. Which of the following is a key condition for this approximation to be valid?

Question 4

The number of customers arriving at a shop in a $30$-minute interval follows a Poisson distribution with a mean of $4$ customers. What is the probability that exactly $5$ customers arrive in a $30$-minute interval?

Question 5

A factory produces light bulbs, and the probability of a bulb being defective is $0.002$. If a sample of $1000$ bulbs is taken, what is the expected number of defective bulbs in the sample, assuming a Poisson approximation to the Binomial distribution?