A supplier sells synthetic fibers to a manufacturing company. A simple random sample of 81 fibers is

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A supplier sells synthetic fibers to a manufacturing company. A simple random sample of 81 fibers is selected from a shipment. The average breaking strength of these is 29 lb, and the standard deviation is 9 lb.
a. Find a 95% confidence interval for the mean breaking strength of all the fibers in the shipment.
b. Find a 99% confidence interval for the mean breaking strength of all the fibers in the shipment.
c. What is the confidence level of the interval (27.5, 30.5)?
d. How many fibers must be sampled so that a 95% confidence interval specifies the mean to within ±1 lb?
e. How many fibers must be sampled so that a 99% confidence interval specifies the mean to within ±1 lb?
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