Question

Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 7. He received a score of 73 on a biology test for which the class mean was 70 with standard deviation 7. On which test did he do better relative to the rest of the class?
biology test
history test
the same

Answer 1

Answer:

history test

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

He did better relative to the class in the test in which he had a higher Z score.

So:

History

Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 7. So we have $X = 75, \mu = 70, \sigma = 7$

So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{75 - 70}{7}$

$Z = 0.71$

Biology

He received a score of 73 on a biology test for which the class mean was 70 with standard deviation 7. So we have $X = 73, \mu = 70, \sigma = 7$

So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{73 - 70}{7}$

$Z = 0.43$

He had a higher Z score in the history test, so this is the test in which he did better relative to the rest of the class.