# 7.2.2 - Proportion 'Greater Than'

7.2.2 - Proportion 'Greater Than'The following two examples use Minitab to find the area under a normal distribution that is greater than a given value. The first example uses the standard normal distribution (i.e., *z* distribution), which has a mean of 0 and standard deviation of 1; this is the default when first constructing a probability distribution plot in Minitab. The second example models a normal distribution with a mean of 65 and standard deviation of 5.

Later in this lesson we'll see that these methods can be used to identify *p* values when conducting right-tailed hypothesis tests.

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Minitab^{®}
– Proportion Greater Than a Value on a Normal Distribution

**Question**: What proportion of the standard normal distribution is greater than a z score of 2?

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
*Right tail* - For
*X value*enter 2 - Click
*Ok* - Click
*Ok*

This should result in the following output:

The area of the z distribution that is greater than 2 is 0.02275.

This could also be written in probability notation as P(z > 2) = 0.02275.

##
Minitab^{®}
– Proportion Greater Than a Value 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 more than 73 mph?

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

To calculate a probability for values **greater than** a given value in Minitab:

- 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
*Right tail* - For
*X value*enter 73 - Click
*Ok* - Click
*Ok*

This should result in the following output:

On a normal distribution with a mean of 65 and standard deviation of 5, the proportion greater than 73 is 0.05480.

In other words, 5.480% of vehicles will be going more than 73 mph.

# 7.2.2.1 - Example: P(Z>0.5)

7.2.2.1 - Example: P(Z>0.5)**Question**: What proportion of the z distribution is greater than z = 0.5?

- 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
*Right Tail* - For
*X value*enter 0.5 - Click
*OK*