UpStudy Free Solution:

To determine which driver got better wear relative to their respective tire brands, we can use the concept of z-scores. The z-score measures how many standard deviations a data point is from the mean. The formula for the z-score is:

\[z = \frac { X - \mu } { \sigma } \]

where \(X\) is the observed value, \(\mu \) is the mean, and \(\sigma \) is the standard deviation.

Let's calculate the z-scores for both Nicole's and Yvette's tire lifetimes.

Nicole's Brand A Tires

Mean (\(\mu _ A\)) = 45000 miles

Standard deviation (\(\sigma _ A\)) = 4300 miles

Observed value (\(X_ A\)) = 37000 miles

\[z_ A = \frac { 37000 - 45000} { 4300} = \frac { - 8000} { 4300} \approx - 1.86\]

Yvette's Brand B Tires

Mean (\(\mu _ B\)) = 36000 miles

Standard deviation (\(\sigma _ B\)) = 2020 miles

Observed value (\(X_ B\)) = 35000 miles

\[z_ B = \frac { 35000 - 36000} { 2020} = \frac { - 1000} { 2020} \approx - 0.50\]

Comparing the Z-scores

A higher (less negative) z-score indicates better performance relative to the brand's average. Comparing the z-scores:

Nicole's z-score: \(- 1.86\)

Yvette's z-score: \(- 0.50\)

Since \(- 0.50\) is higher than \(- 1.86\), Yvette's tires performed better relative to the average performance of Brand B tires than Nicole's tires did relative to Brand A tires.

Therefore, relatively speaking, the driver using the Brand B tires got the better wear.

So, the correct answer is:

b. Brand B

Supplemental Knowledge

To determine which driver got better wear relative to their respective tire brands, we can use the concept of Z-scores. The Z-score measures how many standard deviations an individual data point is from the mean. It is calculated using the formula:

\[Z = \frac { X - \mu } { \sigma } \]

where:

\(X\) is the observed value,

\(\mu \) is the mean,

\(\sigma \) is the standard deviation.

A higher (less negative) Z-score indicates that the observed value is relatively better compared to others in its distribution.

For Brand A:

Mean (\(\mu _ A\)): 45000 miles

Standard deviation (\(\sigma _ A\)): 4300 miles

Nicole's tire lifetime (\(X_ A\)): 37000 miles

For Brand B:

Mean (\(\mu _ B\)): 36000 miles

Standard deviation (\(\sigma _ B\)): 2020 miles

Yvette's tire lifetime (\(X_ B\)): 35000 miles

Without guidance or professional assistance, understanding statistical concepts like Z-scores may prove quite challenging - that's where UpStudy statistics solver comes into the picture!