Answer:
The confidence interval on this case is given by:
 (1)
 (1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:

So then the mean for this case is 69.505
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
 represent the sample mean  
 population mean (variable of interest)
 population mean (variable of interest)  
 represent the population standard deviation
 represent the population standard deviation  
n represent the sample size  
Assuming the X follows a normal distribution  
 
The confidence interval on this case is given by:
 (1)
 (1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:

So then the mean for this case is 69.505