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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?

User Tysha
by
6.5k points

1 Answer

3 votes

Answer:

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

Step-by-step 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*1.10) \\ =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

User Nabster
by
6.4k points
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