Probcapacity and Statistics > Typical Distributions > Area to the Right of a z score

How to find the Area to the Right of a z score

Tbelow are a couple of ways to find the location to the ideal of a z-score wright here z is much less than the mean. With any type of word trouble like this, you’ll need to consult the z-table. The z-table offers you the location between points (i.e. the area to the right of a z score). Once you understand just how to review a z-table, finding the location just takes seconds!

Watch the video for an example:
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You are watching: Find the area in the right tail more extreme than in a standard normal distribution.

If you are in search of various other variations of word troubles prefer this (for example, finding the location for a value between 0 and any kind of z-score, or between two z-scores, see the normal distribution curve index). That index additionally includes images of all the different kinds of areas under the curve to assist you through picking the best short article.

How to discover the Area to the Right of a z score: Steps


location to the right of a z-score (z is less than the mean)

Step 1: Split your z-score right into two, after the tenths decimal location. For example, 0.46 becomes 0.4 + 0.06.

Step 2: Look in the z-table for the given z-value. In order to look up a worth in the z-table, find the intersection. The table listed below shows the outcome for 0.46 (0.4 in the left hand also column and 0.06 in the top row. The interarea is .1772).

Step 3: Add 0.500 to the z-worth you just found in action 2.

That’s it!

Note: Since the graphs are symmetrical, you have the right to overlook the negative z-worths and also simply look up their positive counterparts (in other words, their absolute value). For example, if you are finding a space to the appropriate of a z score and also the area of a tail on the left is -0.46, simply look up 0.46.

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Why am I Adding 50%?

Unfortunately, tbelow are many kind of variations on z-tables in textpublications. However, every one of them work-related on the same assumption that the location under the graph of a normal distribution equals 100%. You might view a whole z-table from -3 to 3, or you could watch 2 halves (like the ones I use on this site). You’ll understand if you’re utilizing a half table if the z-values variety from zero to 3+.

You’re adding the .500 here bereason that’s the entirety location of the right side of the graph (i.e. fifty percent of 100% is 50%). You have to add that to your calculation in order to cover the whole area (the yellow area in the top image). The golden rules:

Almeans sketch a graph,Almeans check which z-table you’re making use of.

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