Question

Question Help The mean finish time for a yearly amateur auto race was 185.64 minutes with a standard deviation of 0.314 minute. The winning​ car, driven by Sam​, finished in 185.29 minutes. The previous​ year's race had a mean finishing time of 110.3 with a standard deviation of 0.129 minute. The winning car that​ year, driven by Rita​, finished in 110.02 minutes. Find their respective​ z-scores. Who had the more convincing​ victory?

Answer 1

Sam has the more convincing victory with a greater Zscore value

Explanation:

Given that :

Year 1:

Mean finish time (m) = 185.64

Standard deviation (s) = 0.314

Sam's time (x1) = 185.29

Year 2:

Mean finish time (m) = 110.3

Standard deviation (s) = 0.129

Rita's time (x1) = 110.02

Zscore = (x - mean) / standard deviation

Sam's Zscore :

(185.29 - 185.64) / 0.314

= - 0.35 / 0.314

= −1.114649

= - 1.115

Rita's Zscore :

(110.02 - 110.3) / 0.129

= - 0.28 / 0.129

= −2.170542

= - 2.171

Sam has the more convincing victory with a greater Zscore value