Question

Direction: Answer the following and illustrate each under the normal curve:

1. Compute the probability area to the left of z = -1.25.

2. Compute the probability area above z = 1.

3. Find the probability area between z = -0.25 and z = 1.5.

4. Find the 90th percentile of a normal curve.

5. Compute the upper 5% of the normal curve.

Answer 1

1) $P(Z<-1.25)=0.10565$

2) $P(Z>1)=0.15866$

3) $P(-0.25<Z<1.5)=P(Z<1.5)-P(Z<-0.25)=0.93319-0.40129=0.5319$

4) $P(Z<a)=0.9\implies a=1.282$

5) The upper 5% is interval $(a,+\infty)$ where

$P(Z>a)=0.05\implies a=1.645$