Download Statistics – Exercises #7

Statistics – Exercises #7
1) A manufacturer of paper used for packaging requires a minimum strength of 20
pounds per square inch. To check on the quality of the paper, a random sample of
10 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 know to equal 2 pounds per square inch, and the strength
measurements are normally distributed.
a) What is the approximate sampling distribution of the sample mean of n =
10 test pieces of paper?
b) If the mean of the population of strength measurements is 21 pounds per
square inch, what is the approximate probability that, for a random sample
of n = 10 test pieces of paper, ¯x < 20?
c) What value would you select for the mean paper strength μ in order that P
(¯x < 20) be equal to .001?
2) Suppose a random sample of n = 25 observations is selected from a population
that is normally distributed, with mean equal to 106 and standard deviation equal
to 12?
a) Give the mean and standard deviation of the sampling distribution of the
sample mean ¯x.
b) Find the probability that ¯x exceeds 110
c) Find the probability that the sample mean deviates from the population
mean μ = 106 by no more than 4.