Question 1:
Assume that for some population the mean is 90 and the standard deviation 
is 20. 

1. If the values in the population are normally distributed, complete the 
   following:
   a. What value corresponds to the 20th percentile? 
   b. Consider the value 125. Is this value larger than the value that 
      corresponds to the 95th percentile? Justify your answer.
2. If the values in the population are Student t distributed, with 10 df, 
   what proportion of these values would you expect to be greater than 30?

Question 2:
Assume that for some population the measurement of interest is denoted by
y (e.g. y may be the wait time of database transactions). Let us say the
mean is 200 and the standard deviation is 20.
Note: Clearly state any necessary assumptions in each case.

1. What proportion of samples of size 100 modules would you expect to have a 
   mean less than 195? 
2. What proportion of samples of size 26 modules would you expect to have a 
   mean less than 195?
3. Examine your answers to parts 1. and 2. above. In your own words, explain 
   why the computed proportions are, or are not, different.


Question 3:
A group of HCI students would like to assess SAS usability. They select 
a random sample of thirty-six users and ask each of them to complete a series 
of tasks. 
They discover that the mean time required to complete the tasks is 15 minutes 
with a standard deviation of 9 minutes. 

1. Provide point estimates of the population mean and standard deviation.
   Are any assumptions required?
2. Consider your estimate of the population mean above:
   a. Determine the margin of error for your estimate. 
   b. Construct and interpret an 80% confidence interval.
   c. Determine the minimum sample size needed to estimate the population mean 
      to an accuracy of 1.5 minutes with 99% confidence.