Question

Suppose that Z ∼ N(0, 1), find

(a) P(Z = −0.93)

(b) P(Z > −0.93)

(c) P(Z < 0.25)

(d) P(−2.13 ≤ Z ≤ 1.93)

Answer 1

We will use the standard normal tables to find these probabilities.

a.

$p(Z=-0.93)=0$

This probability is equal to zero because it is related to finding the area under a point(-0.93) which is zero.

b.

$p(Z\gt-0.93)=1-p(Z\lt-0.93)=1-0.1762= 0.8238$

c.

$p(Z\lt0.25)=0.5987$

d.

$p(-2.13\leqslant Z\leqslant1.93)=\phi(1.93)-\phi(-2.13)=0.9732-0.0166= 0.9566$