A fiberspinning process currently produces a fiber whose strength is normally distributed with a mean of 70 N/m2 and standard deviation of 10 N/m2. To ensure that the fiber has the acceptable strength, five samples of fibers are taken every day. If the average strength of five samples goes under 65 N/m2, a problem with fiberspinning process is suspected, and it is inspected. The strength measurements are assumed to be independent. a) If the mean strength of fibers is actually 70 N/m2, what is the probability that the fiberspinning process is inspected? b) If the true mean fiber strength is still 70 N/m2 what standard deviation would ensure that the probability that the fiberspinning process is inspected is 1.0% or less?
A fiberspinning
process currently produces a fiber whose strength is
with a
acceptable strength, five samples of fibers are taken every day. If the average strength of five
samples goes under 65 N/m2, a problem with fiberspinning
process is suspected, and it is
inspected. The strength measurements are assumed to be independent.
a) If the mean strength of fibers is actually 70 N/m2, what is the probability that the fiberspinning
process is inspected?
b) If the true mean fiber strength is still 70 N/m2 what standard deviation would ensure that
the probability that the fiberspinning
process is inspected is 1.0% or less?
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