Question

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Rolling a single die 36 times, keeping track of the "fives" rolled?

Answer 1

A binomial experiment satisfies these four conditions:

• There should be a fixed number of trials
• Each trial is independent of the others
• There can be only two outcomes either success or failure.
• The probability of each outcome remains constant from trial to trial.

In the given case

Number of trials(n)=36

Each outcomes are independent of each other.

All outcomes are equally likely and have probability of outcome of 1/6

The is only two possibilities either outcome of 5 or not 5

Since it satisfies all the required conditions hence it follows binomial distribution.