Question

To introduce her class to binomial distributions, Mrs. Desai gives a 10 -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let $X=$the number of Patti's correct guesses.

1. Show that $X$is a binomial random variable.

Short answer

It has been shown that$X$is a binomial random variable.

Step-by-step solution

Given Information 

Mr. Desai gives $=10$times

$X=$The number of Patti's correct guesses.

Explanation

The algorithm chose correct responses at random, thus one trial should not alter the outcome of the others.

There were ten questions in total.

Each trial has a$0.20$ chance of succeeding.

As a result, this is a binomial situation.

Because it counts the number of successes, $X$is a binomial random variable with$n=10$and $p=0.20$.