\[N \simeq N( 50, 5^2)\]
, \[P( | x -50 | \le a)=0.4\]
/What is
\[a\]
?Removing the modulus sign gives
\[P(-a \le x-50 \le a)=0.4\]
/>br />
From the diagram below \[P(x \lt 20-a)=0.3\]
.
\[z\]
transform gives \[\frac{(20-a)-20}{5} =-0.542 \rightarrow a=2.71 \]
.