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Use Table II to obtain the areas under the standard normal curve required in Exercises 6.59-6.66. Sketch a standard normal curve and shade the area of interest in each problem.

Find the area under the standard normal curve that lies to the right of

a.-1.07

b.0.6

c.0

d.4.2

Short Answer

Expert verified

a. The area under the standard normal curve that lies to the right of-1.07is0.8577

b. The area under the standard normal curve that lies to the right of0.6is0.2743

c. The area under the standard normal curve that lies to the right of0is0.5000

d. The area under the standard normal curve that lies to the right of4.2is0.0000

Step by step solution

01

Part (a) Step 1: Given Information

Under the standard normal, calculate the area lying to the right of-1.07

02

Part (a) Step 2: Explanation

Right-hand area = 1-Left-hand area

Because the given number -1.07is negative, the conventional normal table of negative zscores is applied.

First, go down to -1.0in the right-hand column labeled 'z,'and then across the row to the right.

As a result, the area to the right of -1.07under the standard normal is 1-0.1423=0.8577.

03

Part (b) Step 3: Given Information

Under the standard normal, calculate the area lying to the right of0.6

04

Part (b) Step 4: Explanation

Right-hand area =1-Left-hand area

Because the given quantity 0.6is positive, the typical normal table of positive zscores is employed. First, move down to 0.6in the left hand column labeled zand then across the row to the column labeled 0.00to get 0.7257.

As a result, the area beneath the standard normal to the right of 0.6is 1-0.7257=0.2743

05

Part (c) Step 5: Given Information

Under the standard normal, calculate the area lying to the right of0.

06

Part (c) Step 6: Explanation 

Right-hand area =1-Left-hand area

The typical table is employed. To begin, move down the left hand column labeled' 'z'to 0.0and then across the row to the column labeled '0.00'to get 0.5000.

As a result, the area beneath the standard normal to the right of 0is 1-0.5000=0.5000.

07

Part (d) Step 7: Given Information

Under the standard normal, calculate the area lying to the right of4.2.

08

Part (d) Step 8: Explanation 

Right-hand area =1-Left-hand area

The typical table is employed. To begin, move down the left hand column labeled' z' to 4.0and then across the row to the column labeled' 0.02to get 1.0000.

As a result, the area beneath the standard normal to the right of 0.42is 1-1.0000=0.0000.

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