Chapter 3.2, Problem 3.42E

(a)

To determine

To Calculate: the proportion of observations from a standard normal deviation that satisfies each of the following statement

Explanation of Solution

Given:

  $z>-1.81$

Calculation:

  $\begin{array}{l}z>-1.81\\ \Rightarrow 1-0.351\\ =0.9649\end{array}$

=96.49%

Graph:

Above z=-1.81 it gives 96.94% of the data which is looking forth.

(b)

To determine

To Calculate: the proportion of observations from a standard normal deviation that satisfies each of the following statement

Explanation of Solution

Given:

  $z<2.29$

Calculation:

  $\begin{array}{l}z<2.29\\ \Rightarrow 0.9890\end{array}$

98.90%

Graph:

Below z=2.29 it gives 98.90% of the data which is looking forth.

(c)

To determine

To Calculate: the proportion of observations from a standard normal deviation that satisfies each of the following statement

Explanation of Solution

Given:

  $-1.81\le Z\le -0.47$

Calculation:

  $\begin{array}{l}-1.81\le Z\le -0.47\\ \Rightarrow 0.3192-0.0351\\ =0.2841\end{array}$

=28.41%

Graph:

Between z=-1.81 and z=-0.47 it gives 28.41% of the data which is looking forth.

(d)

To determine

To Calculate: the proportion of observations from a standard normal deviation that satisfies each of the following statement

Explanation of Solution

Given:

  $-1.02\le Z\le 0.65$

Calculation:

  $\begin{array}{l}-1.02\le Z\le 0.65\\ \Rightarrow 0.7422-0.1539\\ =0.5883\end{array}$

=58.83%

Graph:

Between z=-1.02 and z=-0.65 it gives 58.83% of the data which is looking forth.