Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.

a. $z<-2.46$

b. $0.89<z<2.46$

$z<-2.46$

The formula used: Use the complement rule

To find the equivalent probability, use the normal probability table in the appendix.

In the usual normal probability table for $P(z<-2.46)$look for the row that starts with $-2.4$and the column that starts with$.06$

$P(z<-2.46)=0.0069$

Therefore,

Around $0.0069$ of the observations in a standard Normal distribution satisfy$z<-2.46$

$0.89<z<2.46$

To find the equivalent probability, use the normal probability table in the appendix.

The typical normal probability table for $P(z<0.89)$has a row that starts with $0.8$and a column that starts with$.09$

And

The usual normal probability table for $P(z<2.46)$has a row that starts with $2.4$and a column that starts with$.06$

Then

$$\begin{gathered} P(0.89<z<2.46)=P(z<2.46)-P(z<0.89) \\ =0.9931-0.8133 \\ =0.1798 \end{gathered}$$

Therefore,

Around $0.1798$ of the observations in a standard Normal distribution satisfy$0.89<z<2.46$