91Ó°ÊÓ

$z>−1.66$

The formula used: Use the complement rule$P(notA)=1−P\left(A\right)$

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

In the typical normal probability table for $P(z<−1.66)$look at the row that starts with$-1.6$ and the column that starts with$.06$

Then

Use the complement rule,

$P(notA)=1−P\left(A\right)$

For probability

$$\begin{gathered} P(z>−1.66)P(z>−1.66) \\ =1−P(z<−1.66) \\ =1−0.0485 \\ =0.9515 \end{gathered}$$

Therefore,

Around $0.9515$ of the observations in a standard Normal distribution satisfy$z>−1.66$

$−1.66<z<2.85$

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

In the typical normal probability table for $P(z<−1.66)$look at the row that starts with $-1.6$and the column that starts with$.06$

And

The usual normal probability table for $P(z<2.85)$has a row that starts with $2.8$and a column that starts with$.05$

Then

$$\begin{gathered} P(−1.66<z<2.85) \\ =P(z<2.85)−P(z<−1.66) \\ =0.9978−0.0485 \\ =0.9493 \end{gathered}$$

Therefore,

Around $0.9493$of the observations in a standard Normal distribution satisfy $−1.66<z<2.85$