Answer:
The z-scores for which 3% of the distribution's area lies between -z and z is z=0.03761.
Step-by-step explanation:
We have to find the z-score z* for which the following condition is satisfied:
[tex]P(z<|z^*|)=0.03[/tex]
This means that half of the area is at the left of the mean and half is at the right, so we have:
[tex]P(0<z<z^*)=0.03/2=0.015[/tex]
Then, we have:
[tex]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[/tex]
