Question

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. Nash's test. Which student has the higher standardized score

Answer 1

Answer:

Due to the higher z-score, David has the higher standardized score

Step-by-step explanation:

Z-score:

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.

Which student has the higher standardized score

Whoever had the higher z-score.

David:

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So $X = 52, \mu = 70, \sigma = 11$

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

$Z = \frac{52 - 70}{11}$

$Z = -1.64$

Steven:

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So $X = 52, \mu = 64, \sigma = 6$

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

$Z = \frac{52 - 64}{6}$

$Z = -2$

Due to the higher z-score, David has the higher standardized score