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A manufacturer of paper used for packaging requires a minimum strength of 1700 g/cm2. To check...

A manufacturer of paper used for packaging requires a minimum strength of 1700 g/cm2. To check on the quality of the paper, a random sample of 13 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The standard deviation σ of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 170 g/cm2, and the strength measurements are normally distributed.

a)  If the mean of the population of strength measurements is 1750 g/cm2, what is the approximate probability that, for a random sample of n = 13 test pieces of paper, x < 1700? (Round your answer to four decimal places.)

b) What value would you select for the mean paper strength μ in order that P(x < 1700) be equal to 0.001? (Round your answer to three decimal places.)

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