Chapter 10: Q. 14 (page 668)

Which of the following is not a property of a binomial setting?
(a) Outcomes of different trials are independent.
(b) The chance process consists of a fixed number of trials, $n$
(c) The probability of success is the same for each trial.
(d) If we use a sample size of $30$ , the binomial distribution will be approximately Normal.
(e) Each trial can result in either a success or a failure.

Short Answer

Expert verified

(d) If we use a sample size of 30, the binomial distribution will be approximately Normal. This is not a property of a binomial setting.

Step by step solution

Introduction

Binomial Distribution is the discrete distribution that has the parameter sample size, n, and probability of getting success, p. The binomial distribution is the sum of n independent Bernoulli's distribution with parameter, p.

Explanation

A trial is said to be in a binomial setting if it satisfies the following assumption:

1. Each trial has only one outcome.

2. The probability of success is the same for each trial.

3. Each trial is independent or mutually exclusive.

(a)

The outcomes of each trial are independent. So, it follows the assumption of binomial setting.

(b)

The same size is fixed. So, it follows the property of the binomial setting.

(e)

There are only two possible outcomes that are success or failure. It means each trial is Bernoulli's trial. So, it follows the property of the binomial setting.

(d)

Clearly, it does not follow any assumption of the binomial distribution.

Therefore, (d) is not a property of the binomial setting.