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:

Ait ships the production because 480 is close to 500
Bit doesn’t ship because 480 is less than 500
Cit ships because 480 is within 2.57 standard deviations of 500
Dit does not ship because 480 is more than 2.57 deviations from 500

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Verified Answer :

sethrose sethrose · Answer 1 · 2016-11-09T17:14:12-05:00

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

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AlonsoDehner AlonsoDehner · Answer 2 · 2019-06-27T00:51:12-04:00

Answer:

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

Step-by-step explanation:

Sample size n =30

x bar = 480 : std dev s = 1

Population std dev = sigma = 6

std error of sample = \(\frac{6}{\sqrt{30} } \\\\=1.095\)

Test statistic = \(\frac{480-500}{\frac{6}{\sqrt{30} } }\)

=\(\frac{-20}{1.095}\)=-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