7.2.4 - Proportion 'More Extreme Than'

Minitab 18

Minitab®  – Proportion More Extreme than a z Score

Question: What proportion of the standard normal distribution is more extreme than a z value of ±2?

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 Equal Tails
  6. For X value enter 2 or -2*
  7. Click Ok
  8. Click Ok

* By default, "equal tails" will result in a symmetric distribution. In other words, the same proportion will be in the left and right tails.

This should result in the following output:

Minitab output of a z distribution showing the area less than a z score of -2 and greater than a z score of +2

To find the total proportion of the z distribution that is more extreme than a z value of ±2 we need to add together the area in the two tails: 

0.02275 + 0.02275 = 0.0455

The area that is more than two standard deviations from the mean on a normal distribution is 0.0455, or 4.55%.

Video Walkthrough

Minitab 18

Minitab®

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 proportion of vehicles are deviating from the mean by 10 mph or more? In other words, what proportion are going less than 55 mph or more than 75 mph?

Let's construct a normal distribution with a mean of 65 and standard deviation of 5 to find the area more than 10 mph from the mean.

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 Equal Tails
  6. For X value enter 55 or 75*
  7. Click Ok
  8. Click Ok

* By default, "equal tails" will result in a symmetric distribution. In other words, the same proportion will be in the left and right tails.

This should result in the following output:

Minitab output of a normal distribution with mean of 65 and standard deviation of 5 showing the area less than 55 and greater than 75

To find the total proportion of vehicles that are deviating from the mean by 10 mph or more we need to add together the area in the two tails: 

0.02275 + 0.02275 = 0.0455

The proportion of vehicles deviating from the mean by 10 mph or more is 0.0455, or 4.55%.

Video Walkthrough