Question:

a) You check the statistics for a local 5km race and write down the time it took for everyone to complete the race, then calculate the mean and standard deviation. You note that your friend's time was 40.7 minutes and calculate this is 1.5 standard deviations above the mean. Your friend asks you what the average running time (mean) was but you cannot remember; however, you do recall that the standard deviation was 3.8. Calculate the mean time to finish the race for the entire group.

b) If the grades on a test has a mean of 68.3 (SD = 12.4) how many standard deviations above the mean would you have to be if you wanted to be in the top 4% of your class?

c) What actual mark would need to be in the top 4% of the class?