## Normal Distribution - Within a of the Mean Problem

Suppose for a normally distributed random variable
$N \simeq N( 50, 5^2)$
,
$P( | x -50 | \le a)=0.4$
/
What is
$a$
?
Removing the modulus sign gives
$P(-a \le x-50 \le a)=0.4$
/>br /> From the diagram below
$P(x \lt 20-a)=0.3$
.

Using the normal distribution tables and applying the
$z$
transform gives
$\frac{(20-a)-20}{5} =-0.542 \rightarrow a=2.71$
.