Answer:
a)  
  
 
  
So on this case the 99% confidence interval would be given by (13.83;28.17)  
b) 
c) 
d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.
Step-by-step explanation:
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".  
Part a
 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=350 represent the sample size  
99% confidence interval  
The confidence interval for the mean is given by the following formula:  
 (1)
 (1)  
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: "=-NORM.INV(0.005,0,1)".And we see that
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".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 (13.83;28.17)  
Part b
The margin of error is given by:

Part c
The margin of error is given by:

Part d
As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:
D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.