# 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.

## 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.

Steps
1. From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
2. Check that the Mean is 0 and the Standard deviation is 1
3. Select Options
4. Select A specified x value
5. Select Right tail
6. For X value enter 2
7. Click Ok
8. 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.

Video Walkthrough

## 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:

Steps
1. From the tool bar select Graph > Probability Distribution Plot > One Curve > View Probability
2. Change the Mean to 65 and the Standard deviation to 5
3. Select Options
4. Select A specified x value
5. Select Right tail
6. For X value enter 73
7. Click Ok
8. 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.

Video Walkthrough

# 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?

Steps
1. In Minitab select Graph > Probability Distribution Plot > One Curve > View Probability, hit OK.
2. Select Normal and enter 0 for the mean and 1 for the standard deviation.(Note: The default is the standard normal distribution)
3. Select Options
4. Select A specified x value
5. Select Right Tail
6. For X value enter 0.5
7. Click OK

The proportion of the z distributions that falls above 0.5 is 0.3085.

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