Chapter 6.1, Problem 1E

To determine

To State:

Whether the given statement is true or false.

Answer to Problem 1E

Solution:

The given statement “there are a limited number of normal distributions” is false because there are innumerable number of normal distributions.

Explanation of Solution

Given:

The statement “there are a limited number of normal distributions.”

In statistics, a measurable function that is used to represent outcomes or occurrences of random phenomenon as real numbers is known as a random variable.

In the normal distribution (also known as Gaussian or Gauss-Laplacian) distribution, the probability density function is given by:

$f\left(x|\mu ,{\sigma }^2\right)=\frac{1}{\sqrt{2\pi {\sigma }^2}}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}$

Where $x$ is the value of the random variable while $\mu$ is its mean and ${\sigma }^2$ is the variance.

The normal distribution is the most abundantly found continuous probability distribution function and the real world hosts a milieu of the variables that are normally distributed.

In every field of study, innumerable variables can be found to be following the Gaussian distribution.

Conclusion:

The given statement “there are a limited number of normal distributions” is false because there are innumerable number of normal distributions.