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.

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.

The correct option is  D

Step-by-step explanation:

From the question we are told that

  The mean of the current year  is  

   The standard deviation is  

   The time taken by  the winning car for the current year  is  

  The mean of the previous  year  is  

   The standard deviation the previous  year  is  

 The time taken by  the winning car for the previous year  is      

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

=>    

=>

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

=>    

=>

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

3x3 = 9 and 2x2 = 4

step-by-step explanation: