Supervisor Robert Hall wants to determine the percent of time a machine in his a

Question

Supervisor Robert Hall wants to determine the percent of time a machine in his area is idle. He decides to use work sampling, and his initial estimate is that the machine is idle 22% 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 Hall to be 95.00% confident that the results will be less than 5% from the true result == __(Round your answer to the immediate higher whole number)

Explanation / Answer

Number of Observations, N = Z2pq/E2, E = s*p,

Where Z = 1.65 for 95% confidence level . value of Z can be referred to in Standard Noraml Table or can be calculated by Excel function NORMSINV(0.95)

p = 0.22 (probability of idel time)

q = 1 - p = 0.78

s = 0.05

E = 0.05*0.22 = 0.011

N = 1.962 * 0.22 * 0.78 / 0.0112 = 5448

The number of observations that need to be taken by Hall to be 95.00% confident that the results will be less than 5% from the true result = 5448

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