Question

The mean finish time for a yearly amateur auto race was 186.32 minutes with a standard deviation of 0.305 minute. The winning​ car, driven by Roger​, finished in minutes. The previous​ year's race had a mean finishing time of with a standard deviation of minute. The winning car that​ year, driven by ​, finished in minutes. Find their respective​ z-scores. Who had the more convincing​ victory? had a finish time with a​ z-score of nothing. had a finish time with a​ z-score of nothing.

Answer 1

Complete Question

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

Find their respective z-scores.

Who had the more convincing victory?

A. Roger​ had a more convincing victory because of a higher z-score.

B. Karen a more convincing victory because of a higher z-score.

C. Roger had a more convincing victory, because of a lower z-score.

D. Karen a more convincing victory because of a lower z-score.

Answer:

The correct option is D

Explanation:

From the question we are told that

The mean of the current year is
`\mu_c = 186.32 \ minutes`

The standard deviation is
`\sigma_c = 0.305 \ minutes`

The time taken by the winning car for the current year is
`x = 185.85 \ minutes`

The mean of the previous year is
`\mu_p = 110.7 \ minutes`

The standard deviation the previous year is
`\sigma_p = 0.115 \ minutes`

The time taken by the winning car for the previous year is
`y = 110.48 \ minutes`

Generally the z-score for current year is mathematically evaluated as

`z_c = (x- \mu_c)/(\sigma_c )`

=>
`z_c = ( 185.85- 186.32)/(0.305 )`

=>
`z_c = -1.536`

Generally the z-score for previous year is mathematically evaluated as

`z_p = (y- \mu_p)/(\sigma_p )`

=>
`z_p = ( 110.48-110.7)/(0.115 )`

=>
`z_p = -1.913`

From the value obtained we see that
`z_p < z_c` , Hence Karen had a more convincing victory because of the lower z -score.