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 13 cm with a standard deviation of 0.05 cm. for what lengths will a bolt be destroyed?

select the correct choice below and fill in the answer box(es) to complete your choice.
(round to one decimal place as needed.)
a. a bolt will be destroyed if the length is between □ cm and □ cm.
b. a bolt will be destroyed if the length is less than □ cm.
c. a bolt will be destroyed if the length is less than □ cm or greater than □ cm.
d. a bolt will be destroyed if the length is greater than □ cm.

Explanation:

Step1: Calculate lower cutoff

$\text{Mean} - 2\times\text{Standard Deviation} = 13 - 2\times0.05 = 12.9$

Step2: Calculate upper cutoff

$\text{Mean} + 2\times\text{Standard Deviation} = 13 + 2\times0.05 = 13.1$

Step3: Identify valid range rule

Bolts are destroyed if length is outside the range, i.e., less than the lower cutoff or greater than the upper cutoff.

Answer:

C. A bolt will be destroyed if the length is less than 12.9 cm or greater than 13.1 cm.