For the standard normal distribution, find the probability that z value associated with the 97th percentile

Question

For the standard normal distribution, find the probability that z value associated with the 97th percentile

Answer 1

The standard normal distribution is also called the bell curve because of its shape. The idea is that you have the mean (which has a Z value of 0) and then three standard deviations to the right of the mean and three to the left. It looks like this:

 

http://www.regentsprep.org/Regents/math/algtrig/ATS2/normal67.gif

 

The Z score represents standard deviations: Imagine for the moment that you have this data set. [2, 4, 6]. The mean is (2+4+6)/3 or 4. The standard deviation is 2.

 

A bell curve would have the following values:

 

z of 0, or the mean=4.

 

1z=4+2

2z=4+2+2

3z=4+2+2+2

 

The same calculations apply to negative Z scores so -2z=4-2-2=0.

 

Z scores can be converted into percentiles. This is a good table:

 

http://assets.openstudy.com/updates/attachments/5141b7e4e4b0d5d99f3e827d-directrix-1363263083814-birdzscore.jpg

 

Now, you want the Z value associated with the 97th percentile. In other words you want the Z value closest to 0.97 on the chart. I'm going with 0.9699 (only .0001 off). That has a Z value of 1.88. That's how you convert. So a Z value of 1.88 is at the 96.99 percentile, which is the closest to the number you need to find.