4. Create a SAS program that will generate 100 realizations from a normal distribution with mean 70 and standard deviation 15. Store the generated data into a variable named normgen.

1. Create a new variable GRADES based on normgen. If the generated value is outside the range 0-100 make sure that you trim the value to be within limits (i.e., set it to the nearest limit).

2. Test for normality of the variable GRADES using an appropriate SAS procedure. Produce the normal probability plot and obtain the Shapiro-Wilk test for normality. Interpret your results. Is the new variable normally distributed?

3. Using an appropriate SAS procedure, obtain ONLY the mean, variance, minimum and maximum values for both variables and comment on your findings. Are the values the same?

4. Create a new variable called LETTER that contains the coded grade value as follows: LETTER is A, when GRADES is 90 and above, B, if GRADES is in the interval [80,90), C, if GRADES is in [70,80), D, when GRADES is in [60,70) and F if GRADES is below 60.

5. Use Proc FREQ to obtain a frequency table for the variable LETTER and perform the Chi Square test. What is being tested in this case? Comment on your findings.

6. Create a new data set, call it GRADEDATA, containing variables GRADES and LETTER only, and produce a report (proc print) with the variables GRADES and LETTER only (no other column). Use the labels 'Grades' and 'Letter' to describe the variable names and the title 'Grade results'.