Statistics How To

Area Under a Normal Distribution Curve Index

Critical Values > Area Under a Normal Distribution Curve

How To Find the Area Under a Normal Distribution Curve

How you find the area under a normal distribution curve depends on what your shaded area looks like. Before you can solve for the area under a normal distribution curve, you must be able to imagine what you area looks like. The best (albeit optional) way to imagine this is to make a sketch. For example, let’s say you were give a z-score and were asked to find the area between that score and z=0 (the mean). Your sketch might look like this:

area under a normal distribution curve

Find an area under a curve from z=0 to z=?

There are seven ways your sketch could look, depending on what values you were given. Once you have drawn your sketch, look at the pictures below. Click on the image that looks like your sketch. the link will take you to a step-by-step guide on how to find the area under a normal distribution curve for that shape. Many of these also have short videos showing the steps.

Choose One

area under a normal distribution curve

Find an area under a curve from z=0 to z=?

Area under a normal distribution curve (one tail)

Find an area in one tailed distribution (left or right)

area between two z scores on one side of the mean

area between two z scores on same side

normal distribution with z-values on opposite sides of mean

area between two z values on opposite sides of mean

area to the left of a z-score

area left of a z score (z is greater than the mean)

area to the right of a z-score

area to the right of a z score (z is greater than the mean)

area under a normal distribution curve--two tails

area under a two tailed normal curve

Tip: Drawing sketches in probability and statistics isn’t just limited to normal distribution curves. If you get used to making a sketch, you’ll also have an easier time with creating complicated graphs (like contingency tables).

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Area Under a Normal Distribution Curve Index was last modified: October 12th, 2017 by Stephanie

4 thoughts on “Area Under a Normal Distribution Curve Index

  1. Jill D.

    I bought your book but I’m not sure where to look for the following step-by-step problem solver. I’m on chapter 8 sections 8.1 & 8.2(Statistics Informed Decisions Using Data, M. Sullivan, III). I can solve part a) to the questions but then get lost (my answers aren’t matching the text answers). Here is an example: 8.2 #17 b)What is the probability that in a random sample of 500 adult Americans less than 38% believe that marriage is obsolete? (Note: 39% is the ‘mean’ or P; p-hat?) The text answer is P(‘p hat’ < 0.38)=0.3228 [Tech: 0.3233]* (*I'm allowed to use my TI-84plus calculator too).
    where do I look in my 'Practically Cheating Handbook'? Please guide me. I'm hoping you can help (soon). Thanks!

  2. Andale

    It looks like this problem is using the z-table or t-table. Does the question give you the standard deviation?

  3. malar

    Hi..
    how to find the area of p (0<z<0.855)
    I can be able to find 0.85 only. How to find for 0.005. Pls help me