Question

Find the areas under the normal curve in each of the following cases: (2pts. each)

1. Between z = 0 and z = 1.63 2. Between z = 0 and tau = 0.98

3. To the right of z= 0.29

4. To the left of

5. Between z=-1.56 and z=-1.83

z = - 1.39

Answer 1

1.

$$P(0<Z<1.63) = P(Z<1.63) – P(Z<0)$$

$$=0.948449-0.5=0.448449$$

2.

$$P(0<Z\le0.98) = P(Z\le0.98) – P(Z\le0)$$

$$=0.836457-0.5=0.336457$$

3.

$$P(Z>0.29) = 1-P(Z\le0.29)$$

$$=0.385908$$

4.

$$P(Z<-1.39) =0.082264$$

5.

$$P(-1.83<Z<-1.56) = P(Z<-1.56)$$

$$– P(Z\le-1.83)=0.0593799-0.0336250$$

$$=0.025755$$