A student scores 74 on a geography test and 249 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5. The mathematics test has a mean of 300 and a standard deviation of 34. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class?

We have been given that a student scores 74 on a geography test. The geography test has a mean of 80 and a standard deviation of 5. The student scores 249 on a mathematics test. The mathematics test has a mean of 300 and a standard deviation of 34.

Let us find z-scores for both data points. The z-score tells that a data point is how many standard deviation above or below mean.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

z = z-score,

x = Sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

[tex]z=\frac{74-80}{5}[/tex]

[tex]z=\frac{-6}{5}[/tex]

[tex]z=-1.2[/tex]

Let us find z-score for mathematics test score.

[tex]z=\frac{249-300}{34}[/tex]

[tex]z=\frac{-51}{34}[/tex]

[tex]z=-1.5[/tex]

Since z-score for geography test is [tex]-1.2[/tex], so student was 1.2 standard deviation below mean.

Since z-score for mathematics test is [tex]-1.5[/tex], so student's score was 1.5 standard deviation below mean.

Therefore, the student did better on geography test relative to the other students in each class.