Sampling Distribution Problems:

A colleague at a local company is interested in the performance 
of an image encoding algorithm. Let us consider the time (y) in
milliseconds to encode images of a certain size.

Let us say that for a population of these images the following 
parameters apply:

       Mean: mu(y)=150 milliseconds
       Standard deviation: sigma(y)=40 milliseconds

Considering samples selected from this population, complete the following. 
Make and state any necessary assumptions.

1. For samples of size n=400, what proportion of samples would you expect to 
   result in sample means between 148 milliseconds and 152 milliseconds.

2. For samples of size n=100. 
   a) What proportion of samples would you expect to result in sample means 
      greater than 155 milliseconds. 
   b) What proportion of samples would you expect to result in sample means 
      less than 140 milliseconds. 

3. Let us say the sample size is n=17 instead of n=100. Would this change
   in sample size affect your answer to question 2 above. Justify your
   answer in each case. That is, if your answer is yes, determine the
   new proportion(s). If your answer is no, briefly explain why your answer
   would not be different.