Question

Find the probabilities of the following.

1. 𝑃(𝑧 > 1.36)

2. 𝑃(𝑧 < 2.45)

3. 𝑃(1.2 < 𝑧 < 1.4)

4. 𝑃(−2.75 < 𝑧 < −0.56)

5. 𝑃(𝑧 > −1.05)

Answer 1

1. $P(z>1.36)=1-P(z\leq 1.36)$

$$\approx1-0.913085\approx0.086915$$

2. $P(z<2.45)\approx0.992857$

3. $P(1.2<z<1.4)=P(z<1.4)-P(z\leq 1.2)$

$$\approx0.9192433-0.8849303\approx0.034313$$

4. $P(-2.75<z<-0.56)=P(z<-0.56)-P(z\leq -2.75)$

$$\approx0.2877397-0.0029798\approx0.284760$$

5. $P(z>-1.05)=1-P(z\leq -1.05)$

$$\approx1-0.146859\approx0.853141$$