During a time study, the following times were observed for a particular job using the continuous (non-snapback) method: 22, 51, 72, 98, 128, and 150 seconds. There is only one element per cycle. The sample standard deviation of the observed times has already been computed as 3.9 seconds. If an estimate for the average time that is within 4 percent of the True long-range average 95 percent (z = 1.96) of the time is desired, how many additional observations are needed?
A) fewer than or equal to 40
B) greater than 40 but fewer than or equal to 55
C) greater than 55 but fewer than or equal to 70
D) greater than 70

Question

Quizplus · Accepted Answer

To estimate the needed number of cycles, we need to use the formula:

n = [(z*σ)/(d)]^2

where:
- z is the z-score for the desired level of confidence ( z = 1.96 for 95% confidence)
- σ is the sample standard deviation
- d is the maximum allowable error, which is given as 4% of the True long-range average

Substituting the given values, we get:

n = [(1.96*3.9)/(0.04*μ)]^2

where μ is the True long-range average.
Solving for n, we get:

n = 55.45 ≈ 56

This means that at least 56 cycles are needed to estimate the True long-range average with the desired level of accuracy.

Since we already have 6 observations, we need 56 - 6 = 50 additional observations.

Therefore, the answer is C, as it is the only choice that is greater than 55 but fewer than or equal to 70.

During a Time Study, the Following Times Were Observed for a Particular