Answer
0.0324 (3.24%) of the rods will be discarded
Work Step by Step
$\mu$ = 25, $\sigma$ = 0.07
Want to find $P( x < 24.85 )$
i) Convert 24.85 to a z-score:
z = $\frac{x - \mu}{\sigma}$ = $\frac{24.85 - 25}{0.07}$ = -2.14
ii) $P(x < 24.85) = P(z < -2.14) = 0.0162$
Want to find $P( x > 25.15 )$
i) Convert 25.15 to a z-score:
z = $\frac{x - \mu}{\sigma}$ = $\frac{25.15 - 25}{0.07}$ = 2.14
ii) $P(x > 25.15)$
$= P(z > 2.14)$
$= 1 - P(z < 2.14)$
$= 1- 0.9838$
$= 0.0162$
Therefore, $P(x < 24.85) or P(x > 25.15) = 0.0162 + 0.0162 = 0.0324$
