Question from Kilbaha VCE Further Mathematics Trial Examination

[almostdonewithschooling]

hey, could someone help me with this question:

A university English exam has a mean mark of 70% and a standard deviation of 10%. To achieve
honours a student needs at least 90%. If 5000 students sit the exam, how many students would be
expected to get honours?

i did 90-70/10=2%, then i did 2/100 x 5000 which is wrong because the answer is 125

[guac]

To do this question, use the 68-95-99.7% rule.

This rule posits that, in the context of this English exam, 95% of students can be expected to have a mark that is within two standard deviations of the mean. This means that 95% of students can be expected to have a mark between 50% and 90%. Conversely, this implies that 5% of students can be expected to have a mark either below 50% or above 90%. Because we assume that the exam marks are normally distributed, we can thus expect that of this 5% the number of students that got below 50% and the number of students that got above 90% is equal. So, 2.5% of students can be expected to get above 90% in this exam. 2.5% of 5000 is 125, which gives you your answer.

[almostdonewithschooling]

Ohh rightt, thank you so much