# How many printers should be sampled?

The Longmont Computer Leasing Company leases computers and peripherals like laser printers. The printers have a counter that keeps track of the number of pages printed. The company wishes to estimate the mean number of pages that will be printed in a month on its leased printers. The plan is to select a random sample of printers and record the number on each printer's counter at the beginning of May. Then, at the end of May, the number on the counter will be recorded again and the difference will be the number of copies on that printer for the month. The company wants the estimate to be within ±100 pages of the true mean with a 95% confidence level.

a. The standard deviation in pages printed is thought to be about 1,400 pages. How many printers should be sampled?

b. Suppose that the conjecture concerning the size of the standard deviation is off (plus or minus) by as much as 10%. What percentage change in the required sample size would this produce?

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#### Solution Preview

(a) Confidence Level % = 95

z- score = 1.96

Population SD, σ = 1000

Error, E = 100

Sample Size, N = (z * σ / E)^2 = (1.96 * 1000 / ...

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