Bank manager Art Hill wants to determine the percent of time that tellers are wo

Question

Bank manager Art Hill wants to determine the percent of time that tellers are working and idle. He decides to use work sampling, and his initial estimate is that the tellers are idle 15% of the time. (Round all intermediate calculations to at least two decimal places before proceeding with further calculations.,) The number of observations that need to be taken by Hill to be 99.73% confident that the results will not be more than 6% from the true result = | (round your response up to the next whole number.

Explanation / Answer

proportion of tellers who are idle p = 15%

=>

standard error = sqrt( p * (1-p)/n)

n = size of sample

z-score of 99.73% confidence level = 3

margin of error = z-score * standard error

=>

margin of error = 0.06

=>

3 * sqrt(p*(1-p)/n) = 0.06

=>

3 * sqrt( 0.15*0.85/n) = 0.06

size of sample n = 318.75 = 319

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