The following material is from section 6.1 in your textbook.

When working with everyday data, we think of something as following a normal distribution if a histogram of the data is approximately bell shaped/symmetric. For any normal distribution, the defining features are the mean and the standard deviation. The standard normal distribution is the normal distribution where the mean is 0 and the standard deviation is 1. The standard normal random variable is labelled Z.

Finding areas under the standard normal curve

When working with any normal distribution, you should remember the following:

area under the curve = probability = percent

This means that if we want to find probabilities or percentages having to do with a normal curve, we will need to be able to find areas. There are two method for finding the area under a standard normal distribution: the z-table or technology like our calculators.

Using a z-table

There are several types of z-tables. Some show area to the left of z, while others show the area between z and the mean, 0. Your textbook table is the second type. You can download a copy of it here: 212-z-table.pdf

Let's try finding some areas with the table. You should have a copy in front of you as you review this example!

a) Find the area to the left of z = 1.75.

First, sketch a picture of the area you are trying to find. Then, look up the area in the table for z = 1.75. This is the area between 1.75 and 0. Finally, remember that the area to the left of the mean is 0 for a bell shaped/symmetric distribution.

b) Find the area to the right of z = 0.38.

When you draw your picture, you see that the area between 0 and 0.38 isn't what you need. But, you can take advantage of the fact that half the area is on either side of 0.

Let's try one more case that might come up!

c) Find the area between z = –1.3 and z = 0.50.

Remember, the bell curve is symmetric, so the area between 0 and –1.3 is the same as the area between 0 and 1.3. So, look up each z-value as though it were positive.

Click NEXT to see how this is related to probability.