Use tableII to obtain each shaded area under the standard normal curve.

Short Answer

Expert verified

Parta: The required area is, 0.7994.

Partb: The required area is, 0.8990.

Partc: The required area is, 0.0500.

Partd: The required area is,0.0198.

Step by step solution

01

Part a Step 1. Given information

02

Part a Step 2. Let us find the area for the given diagram.

The area under the standard normal curve that lies between -1.28and 1.28equals the area to the left of 1.28minus the area to the left of -1.28. Standard normal table shows that these latter two areas are 0.8997and 0.1003respectively. So, the required area is,0.8997-0.1003=0.7994.

03

Part b Step 1. Given information

04

Part b Step 2.Let us find the area for the given diagram.

The area under the standard normal curve that lies between -1.64and 1.64equals the area to the left of 1.64minus the area to the left of -1.64. Standard normal table shows that these latter two areas are 0.9495and 0.0505, respectively. So, the required area is,0.9495-0.0505=0.8990.

05

Part c Step 1. Given information 

06

Part c Step 2. Let us find the area for the given diagram.

First we need to find the area to the left of -1.96and 1.96. Standard normal table shows that these latter two areas are 0.0250and 0.9750, respectively. The area under the standard normal curve that lies to the right of 1.96is, 1-0.9750=0.0250. Therefore, the area under the standard normal curve that lies to the left of -1.96or to the right of1.96is,0.0250+0.0250=0.0500.

07

Part d Step 1. Given information

08

Part d Step 2. Let us find the area for the given diagram.

First find the area to the left of -2.33and 2.33. Standard normal table shows that these latter two areas are 0.0099and 0.9901,respectively. The area under the standard normal curve that lies to the right of 2.33is, 1-0.9901=0.0099. Therefore, the area under the standard normal curve that lies to the left of-2.33or to the right of2.33is,0.0099+0.0099=0.0198.

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