Find the area under normal standard curve

Question

A. Directions: Find the area under the standard normal curve which lies to the following conditions. Refer to the z-table and to your concept notes for you to be guided.{Hint: To the right means P(x>a), to the left means P(x<a) and between means P(a<x<b)}

1. to the right of z=0.66

2. to the left of z=-1.53

3. to the right of z=-2.34

4. to the right of z=1.30

5. between z=-0.78 and z=0.56

Answer 1

1. N (0.66)=0.7454 (area to the left), so area to right=1-0.7454=0.2546

2. N(-1.53)=0.0630

3. N(-2.34)=1-N(2.34) (area to left), so area to right = 1-(1-N(2.34))=N(2.34)=0.9904

4. N(1.30)=0.9032 (area to left), so area to right=0.0968

5. N(0.78)=0.7823, N(0.56)=0.7123; area between=0.7823-0.7123=0.0700.

All figures correct to 4 decimal places.

Hint: Area to left for increasingly negative Z gets smaller and smaller, so area to right gets bigger and bigger. Area to left for increasingly positive Z gets bigger and bigger, so area to right gets smaller and smaller. The total area under the normal distribution curve is 1 (100%) and the bell curve has two symmetrical halves. If your tables only give probabilities (area to the left of the Z values) for positive values of Z, then the area to the right of the Z values is exactly the same as the area to the left for corresponding negative values. Therefore N(Z<n)=1-N(Z>n) and N(Z<-n)=1-N(Z<n).