Answer:
We know that the total sample is 200, the mean is 70, and the standard deviation is 7.
For the normal distribution, between the mean and one standard deviation, the percentage of the sample is 34.1%, between the mean plus one standard deviation, and the mean plus two standard deviations, the percentage of the sample is 13.6%, and there is a 2.3% from this point in forward.
Then. the total percentage that received a grade greater than 70 is:
34.1% + 13.6% + 2.3% = 50%
So half the students received a grade of 70 or more, and 50% of 200 is:
0.5*200 = 100
Now, the students that have a grade higher than 84 are the ones with two times the standard deviation away from the mean:
Because 70 + 7 + 7 = 70 +14 = 84
So there are 2.3% of students with a grade higher than 84; this is:
0.023*200 = 4.6, that must be rounded (because you can not have a 0.6 of a student)
So around 5 students received a grade higher than 84.
