Question

Exercise 7.2- 12

Determine the total area under the standard normal curve.

1. to the left of z = -2.94 or to the right of z = 2.94

2. to the left of z = -1.68 or to the right of z = 3.05

3. to the left of z = -0.88 or to the right of z = 1.23

Answer 1

(a)

Case 1:

to the left of Z = - 2.94

Table of Area Under Standard Normal Curve gives area from mid value to Z = - 2.94 on LHS = 0.4984

So,

Area to the left of Z = - 2.94 is = 0.5 - 0.4984 = 0.0016

Case 2:

to the right of Z = 2.94

Table of Area Under Standard Normal Curve gives area from mid value to Z = 2.94 on RHS = 0.4984

So,

Area to the right of Z = 2.94 is = 0.5 - 0.4984 = 0.0016

So,

The total area under the Standard Normal Curve to the left of Z = - 2.94 or to the right of Z = 2.94 is = 0.0016 X 2 = 0.0032

So,

Answer is:

0.0032

(b)

Case 1:

to the left of Z = - 1.68

Table of Area Under Standard Normal Curve gives area from mid value to Z = - 1.68 on LHS = 0.4535

So,

Area to the left of Z = - 1.68 is = 0.5 - 0.4535 = 0.0465

Case 2:

to the right of Z = 3.05

Table of Area Under Standard Normal Curve gives area from mid value to Z = 3.05 on RHS = 0.4989

So,

Area to the right of Z = 3.05 is = 0.5 - 0.4989 = 0.0011

So,

The total area under the Standard Normal Curve to the left of Z = - 1.68 or to the right of Z = 3.05 is = 0.0465 + 0.0011 = 0.0476

So,

Answer is:

0.0476

(c)

Case 1:

to the left of Z = - 0.88

Table of Area Under Standard Normal Curve gives area from mid value to Z = - 0.88 on LHS = 0.3106

So,

Area to the left of Z = - 0.88 is = 0.5 - 0.3106 = 0.1894

Case 2:

to the right of Z = 1.23

Table of Area Under Standard Normal Curve gives area from mid value to Z = 1.23 on RHS = 0.3907

So,

Area to the right of Z = 1.23 is = 0.5 - 0.3907 = 0.1093

So,

The total area under the Standard Normal Curve to the left of Z = - 0.88 or to the right of Z = 1.23 is = 0.1894 + 0.1093 = 0.2987

So,

Answer is:

0.2987