MAT 142

Problem Solving PSU7B:

Normal Distribution Not all marathons are the same. Some have challenging hills, weather, and competition. Others are known for being a "fast" course, or "downhill." Finishing any marathon is a challenge; let's compare marathons using z-scores and the normal distribution. Both marathons below are LA Marathons, but on different courses - one was a circular course around the city (2008), and the other one (from 2015) was "from city to the sea".

Data: (from marathonguide.com)

Marathon #1: City of Los Angeles (circular) March 2, 2008 Mean finish time: 5:36:12 = 5.6033 hours Standard deviation: 1:16:11 = 1.2697 hours N = 16,941 finishers

Marathon #2: City of Los Angeles (city to the sea) March 15, 2015 Mean finish time: 5:30:45 = 5.5125 hours Standard deviation: 1:13:09 = 1.2192 hours N = 21,904 finishers

1. Compare the averages (means) of the two marathons: what do they tell you about the two marathons?

2. Compare the standard deviations of the two marathons: what do they tell you about the two marathons?

3. Use the normal distribution table and z-scores to determine what percent of finishers in each marathon finished with times (show your work):

a. under 3 hours

Marathon #1: City of Los Angeles (circular course)

Marathon #2: City of Los Angeles (city to the sea) 3 continued...

Use the normal distribution table and z-scores to determine what percent of finishers in each marathon finished with times (show your work)

b. over 4 hours Marathon

#1: City of Los Angeles (circular course) Marathon

#2: City of Los Angeles (city to the sea)

c. between 3 and 4 hours

Marathon #1: City of Los Angeles (circular course)

Marathon #2: City of Los Angeles (city to the sea)

4. Based on your analysis, what can you conclude about the difficulty of each marathon? Explain your thinking