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  
Removing the modulus sign gives  
\[P(-a \le x-50 \le a)=0.4\]
/>br /> From the diagram below  
\[P(x \lt 20-a)=0.3\]

normal distribution

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

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