Question

A manufacturer of paper used for packaging requires a minimum strength of 1500 g/cm². To check on the quality of the paper, a random sample of 11 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 150 g/cm², and the strength measurements are normally distributed.

(a) What is the approximate sampling distribution of the sample mean of n = 11 test pieces of paper?

The sampling distribution is nonnormal with mean μ and standard deviation 150.

The sampling distribution is normally distributed with mean 11 and standard deviation 150.

    The sampling distribution is normally distributed with mean μ and standard deviation 150/

11

.The sampling distribution is nonnormal with mean μ and standard deviation 150/

11

.

The sampling distribution is normally distributed with mean μ and standard deviation 150.

(b) If the mean of the population of strength measurements is 1550 g/cm², what is the approximate probability that, for a random sample of n = 11 test pieces of paper,

x < 1500?

(Round your answer to four decimal places.)


(c) What value would you select for the mean paper strength μ in order that

P(x < 1500) be equal to 0.001

Answer 1