### Finding the Z-score when the area is given

Always start each new problem from the home screen

Sometimes we want to find the Z-score by using some given area under the curve. The "3:InvNorm(" option is for just such a problem.

Example 1: Say you want to find the Z-score for the upper 20% of a given population. Since you want the upper 20% that means you are at the 80%-ile. On the calculator we will need to go once again to the distributions menu. Go to this screen: (below left)

Arrow down to choice "3 : InvNorm ( " Press (see upper right screen)

Now enter only *1 value.

You mustenter the percentile of the point for which you want the Z-score.

We will press

.8416212335 will be returned. This is the Z-score for the upper 20%.

* [ If you enter "( %-ile , mean , std. Dev.)" the calculator will return the actual value, not the z-score. ]

Example 2 :

Say you know 50% of the area under the curve is between z and -z.

Find z.

Since the Normal Distribution function is symmetrical it must be that of the 50%,

25% is above the mean and 25% is below the mean.

Recall that we must enter the %-ile of the point for which we desire the Z-score.

The mean is in the middle of the curve so its %-ile is 50% and since 25% is above the mean then we want the Z-score for the 75%-ile. ( 50% + 25%)

We see that z = .674