Suppose you know the length of a confidence interval of a population mean is 8.4 and the sample mean (x bar) is 10. Find the margin of error, and the confidence interval

The lenght of the interval correspond to:

And since we know the margin of error we can find the limits for the confidence interval:

Step-by-step explanation:

Previous concepts

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 represent the sample size  

Solution to the problem

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 margin of error is given by:

The lenght of the interval correspond to:

And since we know the margin of error we can find the limits for the confidence interval:

a

step-by-step explanation: