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-mean)/SD

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. Change to percentiles and compare.

Percentile = precent ≤ a score

i don't get what you mean. Can you please explain it to me again.

The Z score is the score in terms of standard deviations.

Percentile indicates proportion of scores that are equal to or below a particular score.

Consulting the previously named table should be able to give the percentile for each score for comparison.

If you still don't understand, you need to start a new post indicating the specific problem you are having.

To determine in which subject Charlotte performed better, we need to compare her scores relative to the mean and standard deviation of each subject.

Let's start by calculating the z-scores for Charlotte's scores in English and Maths. The z-score measures how many standard deviations a particular value is from the mean.

The formula for calculating the z-score is:
z = (x - μ) / σ

Where:
- x is the value we want to find the z-score for (Charlotte's score)
- μ is the mean of the population (mean score for the subject)
- σ is the standard deviation of the population

For English:
x = 68 (Charlotte's score)
μ = 52 (mean score for English)
σ = 10 (standard deviation for English)

Calculating the z-score for English:
z_english = (68 - 52) / 10
= 16 / 10
= 1.6

Now let's calculate the z-score for Maths:
x = 68 (Charlotte's score)
μ = 55 (mean score for Maths)
σ = 8 (standard deviation for Maths)

Calculating the z-score for Maths:
z_maths = (68 - 55) / 8
= 13 / 8
= 1.625

Now that we have the z-scores for both subjects, we can compare them. The higher the z-score, the better the performance relative to the mean.

In this case, Charlotte's z-score for Maths (1.625) is slightly higher than her z-score for English (1.6). This indicates that she performed slightly better in Maths compared to English.

Therefore, Charlotte performed better in Maths than in English.