for a specific type of machine part being produced, the diameter is normally distributed, with a mean of 15.000 cm and a standard deviation of 0.030 cm. machine parts with a diameter more than 2 standard deviations away from the mean are rejected.

if 15,000 machine parts are manufactured, how many of these will be rejected?

Let be the random variable for the part's diameter, and the same variable transformed into one that follows the standard normal distribution. You're looking for the proportion of the parts that lie 2 standard deviations away from the mean, which translates to



Recall the empirical rule, which says that approximately 95% of a normal distribution falls within 2 standard deviations of the mean, or . This means



So out of 15000 parts, you should expect about 5% of them, or about 750 parts to be rejected.