Find z-score such that the area under the standard normal curve to its left is 0.1825

Answer 1

Hello Brooklyn,

This seems like a beginning Statistics question. First of all when it comes to standard normal curve (which looks like a bell curve) any z-score always references the area to the left of it.

So, given that the area 0.1825 is less than 0.5 this means that our z-score will lie on the left part of the curve which mean the z-score will be negative.

Now, how do we find this z-score that corresponds to an area of 0.1825 to the left of it?

Two ways.

Easiest one, If you have a TI-84 Calculator, follow the steps below:

1. press button "2ND" then press button "VARS
2. Now, under "DISTR" menu, look for "invNorm" and select it
3. depending on how your calculator is programmed, just plug in 0.1825 and hit "Enter" multiple times and the answer will come out to be -0.91

Remember z-scores are always rounded to 2 decimal places.

The other method is by searching through the z-score table. You should have that in your textbook or you can simply google one.

find the negative z-scores table. Look inside the table for an area of 0.1825 or close to this number. Once you find it, match that number with corresponding row first and then the column second. This way your z-score will be -0.(RowValue+ColumnValue) which in this case should be z = -0.91

Please note, when you search the table you may not find 0.1825 so just choose the closest number which in this case would be 0.1814

Let me know if you have any question. Thanks!

Best,

Redal.

Answer 2

The area under the curve between –∞ and z is Φ(z) = (1 + erf(z/√2))/2, whose inverse is z = √2erf ⁻¹(2Φ – 1) that at Φ = 0.1825 equals –0.905879.