Question

Heyy, I need to know what the highest z-value for the lowest 10% of observations on the standard normal distribution is. Can someone help please?

Answer 1

You may picture your problem like this:

I'm not sure which distribution table you're using, but this one http://www.six-sigma-material.com/Normal-Distribution.html shows you values for cumulative areas from \(-\infty\) to the right., showing only positive z-values. Since 10% is below 50%, then it is below the mean of 0 (so you'll have negative z-value).

Answer 2

By symmetry of the standard normal, you have that this area is also the same. Since you are given areas of the form \(P(Z\le z)\) and you need to find the z-value for \(P(Z > z)=0.10\) So, \(P(Z\le z) = 1 - P(Z>z)=1-0.10=0.9\). In your table, the closest z-value to 0.9 is 0.8997 or 0.9015. The z-value in between those would be like \(z=1.285\)

So by symmetry of the standard normal, the value you are looking for is \(z=-1.285\) since \(P(Z<-1.285)\approx 0.10\).

If you can use a calculator/software for this problem, then it is easier and you will also get a more exact value.