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Use Table to obtain the areas under the standard normal curve. 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. 2.02.

b. -0.56.

c. -4.

Short Answer

Expert verified

(a) The area under the standard normal that lies to the right of 2.02is localid="1651202506946" 0.0217

(b) Thus, the area under the standard normal that lies to the right of -0.56is localid="1651202518992" 0.7123

(c) Thus, the area under the standard normal that lies to the right of -4is localid="1651202540941" 1.0000

Step by step solution

01

Part(a) Step 1: Given Information

02

Part(a) Step 2: Explanation

The given number 2.02is positive. Therefore, the conventional normal table of positive zscores is applied. To begin, reduce the number in the left hand column labeled 'z' to 2.0and then move across the row to the column labeled '0.02'. The result is 0.9783.

As a result, the area to the right of 2.02under the usual normal is 1-0.9783=0.0217.

03

Part(b) Step 1: Given Information

04

Part(b) Step 2: Explanation

Area to the right =1- Area to the left

The given quantity is negative, the conventional normal table of negative z scores is applied. First, move down to-0.5 in the right-hand column labelled' z ', then across the row to the column labelled' 0.06 ', and you'll get0.2877.

05

Part(c) Step 1: Given Information

06

Part(c) Step 2: Explanation

Area to the right =1- Area to the left

Because the given number -4 is negative, the conventional normal table of negative z scores is applied. To begin, travel down the right hand column labeled 'z' to -4.0 and then across the row to the column labeled '0.00' to obtain the number0.0000.

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