How many observations should be taken to be 95% confident of being within +5% of the actual time a machine is busy if it is believed that the machine is in use 75% of the time?
A)1,200 observations
B)772 observations
C)364 observations
D)289 observations

Question

Quizplus · Accepted Answer

The sample size needed to be 95% confident of being within +5% of the actual time a machine is busy can be calculated using the formula:n = (Z^2 * p * q) / e^2where:n is the sample sizeZ is the z-score for the desired confidence level (95% = 1.96)p is the estimated proportion of time the machine is busy (75% = 0.75)q is the complement of p (1 - p = 0.25)e is the margin of error (5% = 0.05)Plugging in the values, we get:n = (1.96^2 * 0.75 * 0.25) / 0.05^2n = 289.02Therefore, the correct answer is D) 289 observations.

How Many Observations Should Be Taken to Be 95% Confident