Charlotte received a score of 68 on both her English and Maths tests. The mean for English was 52 and the mean for Maths was 55. The standard deviations for English and Maths

were 10 and 8 respectively. In which subject did Charlotte perform better? Explain your decision.

Z score = score in terms of standard deviations.

Z = (score-mean)/SD

Which Z score is highest?

For explanation, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

To determine in which subject Charlotte performed better, we need to compare her scores in English and Maths with their respective means and standard deviations.

First, let's standardize Charlotte's scores by using the z-score formula:

z-score = (observation - mean) / standard deviation

For English:
z-score(English) = (68 - 52) / 10
z-score(English) = 16 / 10
z-score(English) = 1.6

For Maths:
z-score(Maths) = (68 - 55) / 8
z-score(Maths) = 13 / 8
z-score(Maths) = 1.625

Now, let's compare the z-scores. The greater the z-score, the better the performance.

In this case, Charlotte's z-score for Maths (1.625) is slightly greater than her z-score for English (1.6). This indicates that her performance in Maths is relatively better than in English.

Therefore, Charlotte performed better in Maths compared to English.