Question

Determine if the following probability experiment represents a binomial experiment. A random sample of 25 middle school students is​ obtained, and the individuals selected are asked to state their hair length. Choose the correct answer below. A. ​No, this probability experiment does not represent a binomial experiment because the trials are not independent. B. ​No, this probability experiment does not represent a binomial experiment because the variable is​ continuous, and there are not two mutually exclusive outcomes. C. ​Yes, this probability experiment represents a binomial experiment because each trial has two mutually exclusive outcomes. D. ​Yes, this probability experiment represents a binomial experiment because the probability of success is the same for each trial of the experiment.

Answer 1

Determine if the following probability experiment represents a binomial experiment. A random sample of 25 middle school students is​ obtained, and the individuals selected are asked to state their hair length. Choose the correct answer below

B. ​No, this probability experiment does not represent a binomial experiment because the variable is​ continuous, and there are not two mutually exclusive outcomes

Answer 2

Option A) is the right option.

Explanation:

We are given the following information in the question:

A random sample of 25 middle school students is​ obtained, and the individuals selected are asked to state their hair length.

We have to check whether this distribution is a binomial distribution or not.

• The experiment consists of n repeated trials.
• Each trial can have two possible outcomes only.
• The possible outcome can be success or a failure.
• The probability of success, denoted by p, is the same on every trial.
• The trials are independent.

This distribution is not a binomial distribution because the variables are continuous that is hair length is a continuous variable and there are no two mutually exclusive events. Although, the trails are independent but there is nothing that can be considered as success or failure.

Hence, option A is the correct option.