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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.

6.60 Determine the area under the standard normal curve that lies to the left of

a. -0.87.

b.3.56

c. 5.12.

Short Answer

Expert verified

a. The area under the standard normal curve that lies to the left of-0.87is0.1922

b. The area under the standard normal curve that lies to the left of3.56is0.9998

c. The area under the standard normal curve that lies to the left of5.12is1.0000

Step by step solution

01

Part (a) Step 1: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of-0.87

02

Part (a) Step 2: Explanation 

Because the given quantity -0.87is negative, the conventional normal table of negative zscores is applied. To begin, travel down the right-hand column called 'Z'to -0.8and then across the row to the column labeled '0.07'to get 0.1922.

As a result, the region beneath the standard normal to the left of -0.87is 0.1922.

03

Part (b) Step 3: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of3.56

04

Part (b) Step 4: Explanation 

Because the given number 3.56is positive, the typical normal table of positive zscores is employed.

To begin, proceed down the left hand column labeled' zto 3.5and then across the row to the column labeled' 0.06to get 0.9998.

As a result, the region beneath the ordinary normal to the left of 3.56is 0.9998.

05

Part (c) Step 5: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of5.12

06

Part (c) Step 6: Explanation

Because the given quantity 5.12is positive, the typical normal table of positive zscores is employed. To begin, travel down the left hand column labeled' 'z'to 5.1and then across the row to the column labeled 0.02to get 1.0000

As a result, the area beneath the usual normal to the left of 5.12is 1.0000.

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