Question

In Ms. Polakoski's statistics class the mean score on the final exam is 78 points with a standard deviation of 8 points. Carl was enrolled in Ms. Polakoski's class. His score on the final exam was 89.2. In Mr. Curtis' statistics class the mean score on the final exam is 82 points with a standard deviation of 4 points. Ray was enrolled in Mr. Curtis' class. His score on the final exam was 87.6. Who performed better on the final exam relative to their classmates?

Answer 1

On the final exam, Ray and Carl had an equal performance relative to their classmates.

Explanation:

This problem can be solved by looking at the z-score of Carl and Ray. Whoever has the highest z-score performed better on the final exam relative to their classmates.

The Z score formula is given by:

`Z = (X - \mu)/(\sigma)`

In which: X is the grade we are going to find the z-score of,
`\mu` is the mean score and
`\sigma` is the standard deviation.

Carl:

His score on the final exam was 89.2, so
`X = 89.2`.

The mean score on the final exam is 78, so
`\mu = 78`

With a standard deviation of 8 points, so
`\sigma = 8`

Carl's z-score is:

`Z = (X - \mu)/(\sigma) = (89.2-78)/(8) = 1.4`

Now, we look into the z-table. The p-value of
`z = 1.40` is .9192, which means that Carl perfored better than 91.92% of his classmates.

Ray:

His score on the final exam was 87.6, so
`X = 87.6`

The mean score on the final exam is 82 points, so
`\mu = 82`

With a standard deviation of 4 points, so
`\sigma = 4`

Ray's z-score is:

`Z = (X - \mu)/(\sigma) = (87.6-82)/(4) = 1.4`

Now, we look into the z-table. The p-value of
`z = 1.40` is .9192, which means that Ray also perfored better than 91.92% of his classmates.

On the final exam, Ray and Carl had an equal performance relative to their classmates.