Area under the Standard Normal Curve

Question

Directions: Find the area under the standard normal curve to the right of the given z-value.

z=1.7

Answer 1

So - a standard normal curve has mean 0 and standard deviation 1.

There's a great online tool that will show you visuals to aid in your understanding:

http://onlinestatbook.com/2/calculators/normal_dist.html

Because the normal distribution is a probability distribution, the area under the entire curve is equal to 1, and it can't be less than zero. So there are our bounds. The answer has to be between 0 and 1.

If you plug 1.7 into the "above" section of the calculator and hit "recalculate", you can see that everything above 1.7 standard deviations gets shaded in on the graph, for an area of 0.0446. As a probability percentage, this translates to 4.46%.

There are other ways to do this as well. The NORMDIST function in Excel or Google Sheets will give you almost what you need with =normdist(1.7,0,1,TRUE). Just take 1 minus that result to again get 0.0446.

The other, more traditional way to solve this problem is to use a standard normal table of values and find the result at z=1.7. Usually this will show you the left-tail result (like NORMDIST does) and thus you'll again have to do 1 minus the value.