Question #1:

A colleague is interested in evaluating a new image-processing algorithm. Your colleague is particularly interested in the time required to process images of a certain size (i.e. 1152 x 864 pixels). Image-processing times are known to be normally distributed. The population parameters for processing times of images of this size are:

• Mean: 400 milliseconds
• Standard deviation: 60 milliseconds

1. Given the population parameters above, complete the following:
   1. What proportion of processing times would you expect to be between 440 milliseconds and 540 milliseconds.
   2. What time corresponds to the 40^th percentile.
   3. Your colleague tests the algorithm on a particular image and discovers that the processing time is 508 milliseconds. Is this time slower than the 95^th percentile? Justify your answer.
2. Let y denote image-processing times. Given the population parameters above and considering the sampling distribution of ybar, complete the following. Make any necessary assumptions.
   1. What proportion of samples of size n=17 would you expect to have mean processing times less than 370 milliseconds.
   2. Considering samples of size n=8 and samples of size n=64, comment on the following statement. Justify your answer.

The proportion of samples with mean processing time within three standard deviations of the mean is the same for samples of size n=8 as for samples of size n=64.

Question #2:

You are a Y2K consultant and have been asked by the new director of application development at a large company to investigate the cost to fix the Y2K problem. You select a sample of 18 programs from the portfolio of programs and determine the cost, per line of code, to fix each program. You discover that the sample mean is $2.60 with a standard deviation of $0.90.

1. Provide estimates of the population mean and standard deviation.
2. Given your estimates of the population parameters, and assuming cost per line of code is normally distributed, answer the following:
   1. Determine the proportion of programs in the portfolio that you expect to cost more than $2.60 per line of code to fix.
   2. Would you expect any of the programs in the portfolio to cost more than $6.00 per line of code to fix? Justify your answer.