Answer
0.0124 ball bearings will be discarded.
Work Step by Step
Want to find $P( x < 4.95)$
i) Convert 4.95 to a z-score:
z = $\frac{x - \mu}{\sigma}$ = $\frac{4.95 - 5}{0.02}$ = -2.5
ii) $P(x < 4.95) = P(z < -2.5) = 0.0062$
Want to find $P( x > 5.05 )$
i) Convert 5.05 to a z-score:
z = $\frac{x - \mu}{\sigma}$ = $\frac{5.05 - 5}{0.02}$ = 2.5
ii) $P(x > 5.05)
= P(z > 2.5)
= 1 - P(z < 2.5)
= 1- 0.9938
= 0.0062$
Therefore, $P(x < 4.95) or P(x > 5.05) = 0.0062 + 0.0062 = 0.0124$
