Tensile strength is the ability of a material to resist rupture when pressure is applied to it. In the manufacture of a certain woven polypropylene the manufacture process creates a material with a standard deviation of its tensile strength is pounds per square inch (PSI) and distributed normally.
A quality control inspector tests the tensile strength on a random sample of 40 rolls and finds a mean strength of 87.3 pounds.
a. Find a 99% confidence interval (nearest tenth of PSI). Interpret this interval.
b. Suppose the inspector is unhappy with the previous result and would like to resample. How many rolls should be sampled to estimate the mean tensile strength within 1.5 PSI with 95% confidence?