The owner of Touchdown Sports Bar wants to develop a time standard for the task of mixing a specialty cocktail. In a preliminary study, he observed one of his bartenders perform this task seven times with an average of 90 seconds and a standard deviation of five seconds.
How many observations should be made if he wants to be 95.44 percent confident that the maximum error in the observed time is one second?
A) 64
B) 86
C) 100
D) 144
E) 169

Question

The owner of Touchdown Sports Bar wants to develop a time standard for the task of mixing a specialty cocktail. In a preliminary study, he observed one of his bartenders perform this task seven times with an average of 90 seconds and a standard deviation of five seconds.
How many observations should be made if he wants to be 95.44 percent confident that the maximum error in the observed time is one second?
A) 64
B) 86
C) 100
D) 144
E) 169

Quizplus · Accepted Answer

To determine the sample size needed for the time standard, we can use the formula:

n = [(z*s/E)^2]

where:
z = z-score for desired confidence level (in this case, 1.96 for 95.44% confidence)
s = sample standard deviation (5 seconds)
E = maximum allowable error (1 second)

Plugging in the values:

n = [(1.96*5/1)^2] = 96.04

Rounding up to the nearest whole number, we get a sample size of 100. Therefore, the best choice is C.

The Owner of Touchdown Sports Bar Wants to Develop a Time