A methods and measurement analyst wants to develop a time standard for a certain task. In a preliminary study, he observed one worker perform the task six times with an average observed time of 20 seconds and a standard deviation of two 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

  (5)

Replacing into formula (5) we got:

So the answer for this case would be n=16 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

represent the sample standard deviation

n represent the sample size  

Solution to the problem

Since the Confidence is 0.9544 or 95.44%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.0228,0,1)".And we see that

The margin of error is given by this formula:

   (4)

And on this case we have that ME =1 and we are interested in order to find the value of n, if we solve n from equation (4) we got:

  (5)

Replacing into formula (5) we got:

So the answer for this case would be n=16 rounded up to the nearest integer

if i put something wrong your not gonna like it so rather not say nothing.