Question

est scores for a statistics class had a mean of 79 with a standard deviation of 4.5. Test scores for a calculus class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 84 on the statistics test and a 96 on the calculus test. Calculate the z-score for each test. On which test did the student perform better relative to the other students in each class

Answer 1

Answer:

The z-score for the statistics test grade is of 1.11.

The z-score for the calculus test grade is 7.3.

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

In this question:

The grade with the higher z-score is better relative to the other students in each class.

Statistics:

Mean of 79 and standard deviation of 4.5, so $\mu = 79, \sigma = 4.5$

Student got 84, so $X = 84$

The z-score is:

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

$Z = \frac{84 - 79}{4.5}$

$Z = 1.11$

The z-score for the statistics test grade is of 1.11.

Calculus:

Mean of 69, standard deviation of 3.7, so $\mu = 69, \sigma = 3.7$

Student got 96, so $X = 96$

The z-score is:

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

$Z = \frac{96 - 69}{3.7}$

$Z = 7.3$

The z-score for the calculus test grade is 7.3.

On which test did the student perform better relative to the other students in each class?

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class