Question

If Z is a standard normal random variable, what is the value z for which P(0 ≤ Z ≤ z) = 0.35

Answer 1

We have that $P(0 ≤ Z ≤ z) = 0.35$

$P(0 ≤ Z ≤ z) = P(Z\le z) - P(Z\le 0)=P(Z\le z)-0.5 = 0.35$

Hence

$P(Z\le z)= 0.35+0.5=0.85 \implies z = 1.3$ from normal table we find corresponding z value

Answer: 1.3