A sample of 10 chunks of coal from a particular mine found a sample mean density of 1.39 g/m3 with a population standard deviation of 0.78 g/m3. We wish to create a confidence interval for the true mean density of coal from this particular mine. Round all answers to three decimal places.

Step-by-step explanation:

Assuming the following question: Compute a 95% confidence interval using the 2-distribution, as the population standard deviation is known. The bounds of this confidence interval (lower upper) are:

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

population mean (variable of interest)  

s=0.78 represent the sample standard deviation  

n=10 represent the sample size  

Calculate the confidence interval

Since the sample size is large enough n<30. The confidence interval for the mean is given by the following formula:  

  (1)  

The degrees of freedom are given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that

Now we have everything in order to replace into formula (1):

the infinity sign

step-by-step explanation: