Question

A rope factory produces ropes that have been measured to be able to lift 500 pounds, with a standard deviation of 6 pounds. One Monday, the quality department measures the strength of 30 ropes, and finds them to have an average of 480 pounds with a standard deviation of 1 pound. If the plant only ships production that it is 99% sure is able to lift 500 pounds, what does it do with Monday’s production?

Answers:
A. it ships the production because 480 is close to 500
B. it doesn’t ship because 480 is less than 500
C. it ships because 480 is within 2.57 standard deviations of 500
D. it does not ship because 480 is more than 2.57 deviations from 500

Answer 1

It's C. it does not ship because 480 is more than 2.57 deviations from 500

Answer 2

it does not ship because 480 is more than 2.57 deviations from 500

Explanation:

Sample size n =30

x bar = 480 : std dev s = 1

Population std dev = sigma = 6

std error of sample =
`(6)/(√(30) ) \\\\=1.095`

Test statistic =
`(480-500)/((6)/(√(30) ) )`

=
`(-20)/(1.095)`=-18.26

Since test statistic lies outside i.e. below 2.58 we can reject that for 99% it can lift 500 lbs.

Option d) it does not ship because 480 is more than 2.57 deviations from 500