Question 1191685
the marks in english have a mean of 76% with a standard deviation of 7%.
the marks in science have a mean of 84% with a standard deviation of 5%.


jasmine obtained 86% in english and 89% in science.


use the z-score to compare these.


the z-score formula says z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation, in this case.


for english, her z-score formula becomes z = (86 - 76) / 7 = 1.43, rounded to 2 decimal places.
for science, her z-score formula becomes z = (89 - 84) / 5 = 1, no additional rounding required.


a z-score of 1.43 has a greater area under the normal distribution curve to the left of it.
this indicates she scored higher, relative to her peers, in the english course.
while she had a higher score in science, the rest of the class did better too, making her score less higher, relative to her peers.


fyi, a z-score of 1.43 has an area under the normal distribution curve equal to 
.92364 to the left of it and a z-score of 1 has an area under the normal distribution curve equal to .84134.


an area of .92364 to the left of the z-score means she was better than approximately 92% of her peers in english.
an area of .84134 to the left of the z-score means she was better than approximately 84% of her peers in science.


let me know if you have any questions.
theo