Question

How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 98.0 percent if a pilot study yielded these times (minutes): 4.1,4.6,5.1, 4.9, 5.9, and 4.4? The standard deviation is .631 minutes per cycle. (Use the "mean time" value to 2 decimal places and other values to 3 decimal places for intermediate calculations. Round up your final answer to the next whole number.)

Number of work cycles            

Answer 1

margin of Error = Z* standard deviation / (N)^0.5

In the question,

Z for 98% confidence level =2.33

standard deviation=0.631

Margin of error = [(4.1+4.6+5.1+4.9+5.9+4.4)/6]*0.02 =4.83*0.02 =0.097

Margin of Error = Z* standard deviation / (N)^0.5

0.097=2.33*0.631/(n)^0.5

(N)^0.5 =15.157

N=229.73

N=230

Number of work cycle =230