# 7.2.3 - Proportion 'In between'

7.2.3 - Proportion 'In between'In the following examples we will use Minitab to find the area under a normal distribution between two values. The first example uses the *z* distribution and the second example uses a normal distribution with a mean of 65 and standard deviation of 5.

##
Minitab^{®}
– Area Between Two z Values

**Question**: What proportion of the standard normal distribution is between a *z* score of 0 and a *z* score of 1.75?

Recall that the standard normal distribution (i.e., *z *distribution) has a mean of 0 and standard deviation of 1. This is the default normal distribution in Minitab.

- From the tool bar select
*Graph > Probability Distribution Plot > One Curve > View Probability* - Check that the
*Mean*is 0 and the*Standard deviation*is 1 - Select
*Options* - Select
*A specified x value* - Select
*Middle* - For
*X value 1*enter 0 - For
*X value 2*enter 1.75 - Click
*Ok* - Click
*Ok*

This should result in the following output:

The proportion of the z distribution that is between 0 and 1.75 is 0.4599.

In probability notation, this could be written as P(0 ≤ z ≤ 1.75) = 0.4599

##
Minitab^{®}

## Area Between Two Values on a Normal Distribution

**Question:** Vehicle speeds at a highway location have a normal distribution with a mean of 65 mph and a standard deviation of 5 mph. What is the probability that a randomly selected vehicle will be going between 60 mph and 73 mph?

Let's construct a normal distribution with a mean of 65 and standard deviation of 5 to find the area between 60 and 73.

- From the tool bar select
*Graph > Probability Distribution Plot > One Curve > View Probability* - Change the
*Mean*to 65 and the*Standard deviation*to 5 - Select
*Options* - Select
*A specified x value* - Select
*Middle* - For
*X value 1*enter 60 - For
*X value 2*enter 73 - Click
*Ok* - Click
*Ok*

This should result in the following output:

On a normal distribution with a mean of 65 mph and standard deviation of 5 mph, the proportion of observations between 60 mph and 73 mph is 0.7865.

In other words, 78.65% of vehicles will be going between 60 mph and 73 mph.

# 7.2.3.1 - Example: Proportion Between z -2 and +2

7.2.3.1 - Example: Proportion Between z -2 and +2**Question**: What proportion of the z distribution is between -2 and 2?

- In Minitab select
*Graph > Probability Distribution Plot > One Curve > View Probability*, hit*OK*. - Select
*Normal*and enter 0 for the*mean*and 1 for the*standard deviation.*(Note: The default is the standard normal distribution) - Select
*Options* - Select
*A specified x value* - Select
*Middle*and enter- X value 1: -2
- X value 2: 2

- Select
*OK*