Question

A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 7 cm with a standard deviation of 1.10 cm. For what lengths will a bolt be destroyed?

Answer 1

Answer:

Any bolt length lesser than 4.90 cm or greater than 9.10 cm will be destroyed

Explanation:

Given that:

Mean length = 7 cm

Standard deviation = 1.10 cm

Any bolt outside 2 standard deviations is to be destroyed

The bolt lengths that will be destroyed is obtained as shown below:

$\begin{gathered} =\mu\pm n\sigma \\ \mu=7cm \\ n=2 \\ \sigma=1.10cm \\ \text{ } \\ \text{Substitute the variables into the formula, we have:} \\ =7\operatorname{\pm}(2\times1.10) \\ =7\operatorname{\pm}2.10 \end{gathered}$

This therefore means that any bolt length lesser than 4.90 cm or greater than 9.10 cm will be destroyed