Chapter 10, Problem 14PT3

To determine

To identify which is not a property of a binomial setting :

Answer to Problem 14PT3

(d) If we use a sample of size 30, the binomial will be approximately normal

Explanation of Solution

Given information:

Given the 5 statement about the binomial distribution among one is not a property of the binomial and needed to find the same.

A binomial distribution has the following properties:

• The outcomes of the experiment is either a “success” or a “failure”
• There exist n number of identical trials in the experiment
• Success probability remains same in each trial
• The outcomes of the trials are independent

If the above condition satisfied then the random variable is binomial.

Therefore from the given statement we can conclude that (a), (b), (c) and (e) are the same condition mentioned above. Therefore in this context the option (d) is not a property of the binomial setting.

Binomial distribution tends to normal for large values of sample size n by the central limit theorem. Also for small samples, the approximation holds whenever we have $np>5$ and $n(1-p)>5$ provided $p=\frac{1}{2}$