Basis for the Range Rule of Thumb and the Empirical Rule. In Exercise, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage andfill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-3.

About_____ % of the area is between z = −1 and z = 1 (or within 1 standard deviation of the mean).

Answer :

Step 1 :

In finding the area under standard normal curve, you can use the statistical tables at the back of your textbook, or use your calculator.

In using the tables, remember that areas are reported as P(Z < a)

Therefore, you need to use the following relationships

P(Z > a) = 1 - P(Z < a)

P(a < Z < b) = P(Z < b) - P(Z < a)

Applying this principles, we get

P(-1 < Z < 1) =...