Question

Nick is a psychology student who participates in sprint triathlon competitions which consist of swimming, cycling and running in one event. In the last competition, Nick completed the swimming race in 12 minutes and 46 seconds (766 seconds), cycling in 33 minutes and 52 seconds (2032 seconds), and the running race in 17 minutes and 3 seconds (1023 seconds).

Completion times for participants in Swimming are normally distributed with a mean of m = 693 seconds and a standard deviation s = 61 seconds. Completion times for participants in Cycling are normally distributed with a mean of m = 2182 seconds and a standard deviation s = 77 seconds. And completion times for participants in Running are normally distributed with a mean of m = 1080 seconds and a standard deviation s = 50 seconds.

In which competition race (swimming, cycling or running) was Nick’s performance better, relative to others on average who took part in that competition? Justify your answer, quoting relevant statistics as part of your explanation.

Answer 1

Here we need to find z scores for each events.

The formula of z score is as follows:

For swimming

Nick completed the swimming race in 12 minutes and 46 seconds (766 seconds)

so, x = 766

Swimming are normally distributed with a mean of m = 693 seconds and a standard deviation s = 61 seconds.

For cycling

Nick completed the cycling in 33 minutes and 52 seconds (2032 seconds)

So x = 2032

Completion times for participants in Cycling are normally distributed with a mean of m = 2182 seconds and a standard deviation s = 77 seconds.

So,

For running,

Nick completed the running race in 17 minutes and 3 seconds (1023 seconds).

So x = 1023

completion times for participants in Running are normally distributed with a mean of m = 1080 seconds and a standard deviation s = 50 seconds.

So,

The z-score of swimming is 1.20 which is greater than the z-scores of other two competitions.

So that Nick's performance in swimming is better than the cycling and running.