Question

Property $4$of Key Fact $6.5$states that most of the area under the standard normal curve lies between $-3$and $3$. Use Table II to determine precisely the percentage of the area under the standard normal curve that lies between $-3$ and $3$.

Short answer

The area under the standard normal curve as a proportion of the total area $=99.74\%$.

Step-by-step solution

Given Information

Take a look at a standard normal curve.

$0.9987$ is the area to the left of $3$.

$0.0013$ represents the area to the right of $-3$.

Explanation

The area between the two points on the standard normal curve $-3$and $3$is equals to the area to the left of $3$minus area to the right of $-3$.

Then, the area under the standard normal curve

$=0.9987-0.0013$

$=0.9974$

$=99.74\%$

Hence,

A percentage represents the area under the standard normal curve. localid="1650956164362" $99.74\%$