Q.6.55 - Elementary Statistics

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 $3$.

Step-by-Step Solution

Answer

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

Step 1: 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 $-3$.

Step 2: 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. $99.74\%$