# Thread: Statistics: Standard Normal Distribution-Confused

1. ## Statistics: Standard Normal Distribution-Confused

I know that the 1 standard deviation is 68% and a 2 standard is 95 %. What should I do first, in order too set up the problem? I came up with .975, but only from using an calulator. Am i suppose to subtract the numbers or add in the z from the z score table?

Between 1 standard deviation below the mean and 2 standard deviation above the mean.

More than 2 standard deviation away from the mean.

2. Originally Posted by Lydia08
I know that the 1 standard deviation is 68% and a 2 standard is 95 %. What should I do first, in order too set up the problem? I came up with .975, but only from using an calulator. Am i suppose to subtract the numbers or add in the z from the z score table?

Between 1 standard deviation below the mean and 2 standard deviation above the mean.

More than 2 standard deviation away from the mean.
1 SD below accounts for 34% (one half 68) and 2 above account for 34+13.5=47.5%

That is because 95-68=27. 27/2=13.5

You can see from the graph of the normal distribution.

Add them up. one below to two above would be 34+34+13.5=81.5

From the tables, look up z=-1 and z=2. You should get close to 81.5

z=-1 corresponds to .1587. Then, .5-.1587=.3413

z=2 corresponds to .9772. Then, .9772-.5=.4772

.4772+.3413=.8185.

See?. Close to the graph method.

3. There are 15.9% one standard deviation below the mean and 2.2% 2 standard deviation above the mean.
100% - 15.9% - 2.2% = ?