Question

Define, describe, and compare the following questions:

What are a normal distribution and a standard normal distribution?

What are their properties?

Write a good paragraph with at least five (5) sentences using a minimum of 75 words.

Answer 1

A

normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve, which has all of the following properties:

1. The mean, median, and mode are equal.

2. The normal curve is bell-shaped and is symmetric about the mean.

3. The total area under the curve is equal to one.

4. The normal curve approaches, but never touches, the x-axis

5. Between μ-σ and μ+σ

the graph is concave down and elsewhere the graph is concave up. The points at which the graph changes concavity are called inflection points

.

Standard normal distribution has mean = 0 and sd = 1

The whole theory of sample tests t, f and chi-square test is based on the normal distribution.