Answer:
a) And if we replace we got: 

b)  
    
 
    
So on this case the 99% confidence interval would be given by (62.182;93.818)    
Step-by-step explanation:
Dataset given: 109 67 58 76 65 80 96 86 71 72
Part a
For this case we can calculate the sample mean with the following formula:

And if we replace we got: 
And the deviation is given by:

And if we replace we got 
Part b
The confidence interval for the mean is given by the following formula:
 (1)
   (1)
In order to calculate the critical value  we need to find first the degrees of freedom, given by:
 we need to find first the degrees of freedom, given by:
 
Since the Confidence is 0.99 or 99%, the value of  and
 and  , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that  
Now we have everything in order to replace into formula (1):
 
    
 
    
So on this case the 99% confidence interval would be given by (62.182;93.818)