Question

ethel doesnt feel like studying fo her multiple choice exam. the exam contains ten questions and each question has four choices. ethel plans to choose a random answer for each question. what is the distribution of the total number of correct answers

Answer 1

The total number of correct answers follows a Binomial distribution with parameters n = 10 and p = 0.25.

`p_(X)(x)={10\choose x}(0.25)^(x)(1-0.25)^(10-x);\ x=0,1,2,...10`

Explanation:

Let X be defined as the total number of correct answers by Ethel.

There are n = 10 questions in the multiple choice exam.

It is provided that each question has four choices. That is, the probability of selecting the correct option foe each of these 10 questions is, p = 0.25.

As Ethel has not prepared for the exam, she answers all the questions independently of the others.

Thus, the above data explains that the random variable X follows a Binomial distribution with parameters n = 10 and p = 0.25.

The probability mass function of X is:

`p_(X)(x)={10\choose x}(0.25)^(x)(1-0.25)^(10-x);\ x=0,1,2,...10`