How do you find the area under the normal distribution curve to the right of z = –3.24?

Jun 21, 2017

$.9994$ square units or 99.94%

Explanation:

Currently, the information given is the z-score, which is $z = - 3.24$.

Z-scores have an equivalent percentage of the area under the normal distribution curve.

While this table may look very long and confusing to understand, it is actually pretty simple! This purpose of this table is to convert your z-score into its equivalent percentage.

Your z-score is located on the farthest left yellow column $\left(3.2\right)$ The yellow row on top is if you have a z-score with a hundreths value, which you do. $\left(0.04\right)$

First, find the row with the z-score $3.2$. (It's the third row from the bottom.)

Next, look under the column $0.04$.

Third, find where the row and column intersect! It should meet up at $.4994$.

However, this is only the area between the halfway point of the normal distribution curve and your z-score.

Since you want everything to the right of $- 3.24$, you must also add $.5$ to compensate for the other 50% of the graph.

$.4994 + .5$

Your answer is $.9994$ square units, or 99.94%!

Jun 23, 2017

.9994 or 99.94%

Explanation:

If you have a graphing calculator, you can use it to find the area.

Hit 2nd > VARS > 2: normalcdf(

This will prompt you for the lower bound, upper bound, mean ($\mu$), and standard deviation ($\sigma$).

First, fill in your lower and upper bounds. You want to find the area to the right of z = -3.24, which means -3.24 and everything above that. Therefore,

lower bound = -3.24
upper bound = 999

Keep $\mu$ (the mean) as 0 and $\sigma$ (the standard deviation) as 1, since we are dealing with z scores.

Then press paste and enter, and you should get an answer of approximately .9994, or 99.94%.