1. You are interested in the performance of an image compression algorithm.
   Let us say that, for a corpus of images, the mean compression time is
   80ms with standard deviation 20ms. 

   Consider samples of size 64 images that could be selected from this corpus. 
   Given the sampling distribution of ybar, what proportion of samples
   would you expect to result in sample means greater than 91ms.

 
2. A usability analyst is interested in evaluating a browser-based interface.
   She decides to conduct a controlled experiment and selects a sample of 
   seventeen users for observation. She provides them with a suite of tasks
   and observes the number of errors made in completing the task suite. She
   discovers that the mean error count is 15 with standard deviation of 8.

   Given these facts, answer the following questions. Remember to make and  
   state any necessary assumptions in each case.

   a) Provide a point estimate for the mean error count of the population.
   b) Determine the margin of error for your estimate of the population mean.
   c) Construct and interpret an 80% confidence interval for the population 
      mean. 
   c) Construct and interpret a 99% confidence interval for the population 
      mean. 

 
3. You are interested in database performance and would like to estimate
   the mean wait time of transactions processed on a particular day to a 
   level of accuracy of 1.5ms. 

   a) You select a small sample of transactions and discover that the standard
      deviation is 10ms. Determine the minimum sample size required in each 
      case below.
      i) The level of confidence is 90%. 
     ii) The level of confidence is 99%. 
   b) You are unable to selct a small sample to determine the standard
      deviation, as done above, but know from experience that transaction
      wait time ranges between 4ms and 36ms. Use this fact to determine
      the minumum sample size needed to estimate the mean wait time if 
      the level of confidence is 95%.