Question

Find the​ z-scores for which 3​% of the​ distribution's area lies between -z and z.

Answer 1

The​ z-scores for which 3​% of the​ distribution's area lies between -z and z is z=0.03761.

Explanation:

We have to find the z-score z* for which the following condition is satisfied:

`P(z<|z^*|)=0.03`

This means that half of the area is at the left of the mean and half is at the right, so we have:

`P(0<z<z^*)=0.03/2=0.015`

Then, we have:

`P(z<z<z^*)=P(z<z^*)-P(z<0)=0.015\\\\P(z<z^*)=0.015+P(z<0)=0.015+0.5=0.515\\\\\\z^*=0.03761`