Question

Instructions: Imagine you’ve just started training to run a 5k race (it’s approximately 3.1 miles). You’re curious how long it takes other beginners to run that distance, so you ask 17 of your other beginner running friends how long it takes them, and you found the following answers:

Time to complete 5k (in minutes):

23 24 25 25 26 26 27 27 27 27 28 28 29 29 30 31 32

This one is tricky! Imagine that you meet a new friend who is also a beginner, she's extremely fast and can run the 5k in 20 minutes. You wonder what percentage of the beginner running population could run the 5k faster than your new friend (that is, what percentage of the population has a time that is less than your new friend?). (Hint: use Appendix B.1 to answer this question! It might help to draw out a normal distribution, find your friend's z score on the distribution, and then figure out what area you're looking for in the z-table from the appendix).

5%

99.87%

0.13%

10%

Answer 1

First we need to calculate the mean and SD of the time taken by the beginners:

Mean: 27.29

SD: 2.35

Next, we find the friend's z score:

Z: 3.1

Hence, the correct answer is Option C. Only 0.13 percent of the population will have a time less than my friend's.