Chapter 2.2, Problem 60E

(a)

To determine

Proportion of observations in a standard Normal distribution that satisfies the given statement.

Answer to Problem 60E

Around 0.0069 of the observations in a standard Normal distribution satisfy the statement.

Explanation of Solution

Given Information:

  $z<-2.46$

Calculations:

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with -2.4 and the column that starts with .06 of the standard normal probability table for $P\left(z<-2.46\right)$ .

  $P\left(z<-2.46\right)=0.0069$

Therefore,

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

(b)

To determine

Proportion of observations in a standard Normal distribution that satisfies the statement provided.

Answer to Problem 60E

Around 0.1798 of the observations in a standard Normal distribution satisfy the statement.

Explanation of Solution

Given Information:

  $0.89<z<2.46$

Calculations:

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with 0.8 and the column that starts with .09 of the standard normal probability table for $P\left(z<0.89\right)$ .

And

See the row that starts with 2.4 and the column that starts with .06 of the standard normal probability table for $P\left(z<2.46\right)$ .

Then

The difference between the probabilities to the left of the boundaries is the probability between two boundaries.

  $\begin{array}{l}P\left(0.89<z<2.46\right)=P\left(z<2.46\right)-P\left(z<0.89\right)\\ =0.9931-0.8133\\ =0.1798\end{array}$

Therefore,

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