A bank manager wants to determine the percent of time the bank's tellers are working and idle. He decides to use work sampling, and his initial estimate is that the tellers are idle 22% of the time. Approximately how many observations should be taken to be 95% confident that the results will not be more than 5% away from the true result?
A) 6
B) 16
C) 203
D) 264
E) 246

Question

Quizplus · Accepted Answer

We use the formula n = (Z^2 * P * Q) / E^2, where:

- n = sample size
- Z = z-score corresponding to the desired level of confidence (in this case, 1.96 for 95% confidence)
- P = initial estimate of proportion (in this case, 0.22)
- Q = 1 - P
- E = maximum allowable error (in this case, 0.05)

n = (1.96^2 * 0.22 * 0.78) / 0.05^2
n ≈ 263.674

Rounding up, the answer is 264. Therefore, we need to take approximately 264 observations to be 95% confident that the results will not be more than 5% away from the true result. Choice D is correct.

A Bank Manager Wants to Determine the Percent of Time