Question

The total area under the following standard normal curve is divided into eight regions.

a. Determine the area of each region.

b. Complete the following table.

Short answer

(a) The area of each section will be

Area at $1$standard deviation $=34.13\%$

Area at $2$standard deviation $=13.59\%$

Area at $3$standard deviation $=2.28\%$

(b) The area of each section will be

$\begin{array}{ccc}\text{Region}& \text{Area}& \begin{array}{c}\text{Persentage of}\\ \text{total area}\end{array}\\ -\infty \text{to}-3& 0.0013& 0.13\\ -3\text{to}-2& 0.0215& 2.15\\ -2\text{to}-1& 0.1359& 13.59\\ -1\text{to}0& 0.3413& 34.13\\ 0\text{to}1& 0.3413& 34.13\\ 1\text{to}2& 0.1359& 13.59\\ 2\text{to}3& 0.0215& 2.15\\ 3\text{to}\infty & 0.0013& 0.13\\ & 1.0000& 100.00\end{array}$

Step-by-step solution

Part(a) Step 1: Given Information

Part(a) Step 2: Explanation

Using the relation, calculate the standard deviation and mean.

$\sigma =\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}$

$\overline{x}=\frac{\sum x_i}{n}$

We'll get it after we've solved it.

$\sigma =1.78$

$\overline{x}=0$

Then, using the illustration as a guide, determine the area.

Part(b) Step 1: Given Information

Part(b) Step 2: Explanation

Using the relation, calculate the standard deviation and mean.

$\sigma =\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}$

$\overline{x}=\frac{\sum x_i}{n}$

We'll get it after we've solved it.

$\sigma =1.78$

$\overline{x}=0$

Then, using the illustration as a guide, determine the area.