Aprecision control engineer is interested in the mean length of tubing being cut automatically by machine. it is known that the standard deviation in the cutting length is 0.15 feet. a sample of 60 cut tubes yields a mean length of 12.15 feet. this sample will be used to obtain a 99% confidence interval for the mean length cut by machine. develop the 99% confidence interval for population mean.

The 99% confidence interval would be given by (12.10;12.20)

Step-by-step explanation:

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".

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".

represent the sample mean  

population mean (variable of interest)

represent the population standard deviation

n=60 represent the sample size  

Assuming the X follows a normal distribution

The sample mean is distributed on this way:

The confidence interval on this case is given by:

  (1)

The next step would be find the value of , and

Using the normal standard table, excel or a calculator we see that:

Since we have all the values we can replace:

So on this case the 99% confidence interval would be given by (12.10;12.20)  

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step-by-step explanation: