Respuesta :
Answer:
Terry had a finish time with a z-score of -1.45.
Jane had a finish time with a z-score of -2.12. Due to the lower z-score, Jane had the more convincing win.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever's z-score was lower, that is, took less time to complete the race compared to their competitors, had the more convincing win.
Terry:
The mean finish time for a yearly amateur auto race was 185.53 minutes with a standard deviation of 0.339 minute. The winning car, driven by Terry, finished in 185.04 minutes.
This means that [tex]\mu = 185.53, \sigma = 0.339, X = 185.04[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{185.04 - 185.53}{0.339}[/tex]
[tex]Z = -1.45[/tex]
Terry had a finish time with a z-score of -1.45.
Jane:
The previous year's race had a mean finishing time of 111.6 with a standard deviation of 0.104 minute. The winning car that year, driven by Jane, finished in 111.38 minutes.
This means that [tex]\mu = 111.6, \sigma = 0.104, X = 111.38[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{111.38 - 111.6}{0.104}[/tex]
[tex]Z = -2.12[/tex]
Jane had a finish time with a z-score of -2.12. Due to the lower z-score, Jane had the more convincing win.
