Chapter 3, Problem 3.49RE

(a)

To determine

To Calculate: the proportion of observations from a standard normal distribution that falls in each of the following and sketch a standard normal curve.

Explanation of Solution

Given:

  $z\ge -2.25$

Calculation:

  $\begin{array}{c}z\ge -2.25\\ \Rightarrow 1-0.0122\\ =0.9878\\ =98.78\%\end{array}$

Graph:

Above z=-2.25 it gives 98.78% of the data which is looking forth.

(b)

To determine

To Calculate: the proportion of observations from a standard normal distribution that falls in each of the following and sketch a standard normal curve.

Explanation of Solution

Given:

  $-2.25<z<1.77$

Calculation:

  $\begin{array}{c}-2.25<z<1.77\\ \Rightarrow 0.9616-0.0122\\ =0.9494\\ =94.94\%\end{array}$

Graph:

Between z=-2.25 and z=1.77 it gives 94.94% of the data which is looking forth.

(c)

To determine

To Calculate: the proportion of observations from a standard normal distribution that falls in each of the following and sketch a standard normal curve.

Explanation of Solution

Given:

  $z<2.89$

Calculation:

  $\begin{array}{c}z<2.89\\ \Rightarrow 0.9981\\ =99.81\%\end{array}$

Graph:

Below z=2.89 it gives 99.81% of the data which is looking forth.

(d)

To determine

To Calculate: the proportion of observations from a standard normal distribution that falls in each of the following and sketch a standard normal curve.

Explanation of Solution

Given:

  $1.44<z<2.89$

Calculation:

  $\begin{array}{c}1.44<z<2.89\\ \Rightarrow 0.9981-0.9251\\ =0.0730\\ =7.30\%\end{array}$

Graph:

Between z=1.44 and z=2.89 it gives 7.30% of the data which is looking forth.