There are many different types of statistics interview questions that one may see during an interview. Below is an example of a statistics question that I saw when studying.

After reading the above problem, we know we need to calculate the expected value of ads shown in 100 news stories and the probability that a certain amount of ads appear in 100 stories. But before we start answering the question we need to figure out the type of distribution for this question. If you guessed that this is a binomial distribution then you are right. In each option there is a probability of having an ad and a probability of not having an ad and this can be applied to every store. In binomial distribution, to calculate the expected value we would need to calculate *E[ X ] = n p *where *n *is the number of stores and *p* is the probability of having an ad.

- In the first option we have that out of every 25 stories, one will be an ad. Therefore the probability of having an ad would be 1/25 and so the expected number of ads shown in 100 news stories would be 1/25 * 100 =4.
- Similarly in the second option, the probability of a story having an ad is 4%. Therefore the expected number of ads shown in 100 news stories would be 4% * 100 = 4.

To calculate the probability of a binomial distribution we would need to below formula.

Using the second option and the formulas above we can calculate the chance of a single ad being shown in 100 stories.

- n = 100, 100 stories
- x = 1, 1 ad appearance
- p = 0.04, probability of ad appearing
- q = 0.96, probability of no ad appearing

Plugging all the values above into the equation you should get 100 * (0.04)¹ *(0.96)⁹⁹ ≈ 0.07029. Similarly the chance of no ads appearing in 100 stories would be 1 * (0.04)⁰ * (0.96)¹⁰⁰ ≈ 0.01687.

Hope this helps you in your future attempts at solving future statistics problem dealing with calculating expected values and probabilities of Binomial Distribution. For further questions, feel free to email me at andypeng93@gmail.com.