Question

The marks obtained by students of a class in a test are normally distributed with a mean of 60 marks and a standard deviation of 5 marks. About what percent of students have scored more than 65 marks?

a. 2.5
b. 16
c. 34
d. 47.5

Answer 1

About 16% of students scored more than 65 marks, as 65 marks is one standard deviation above the mean in the normal distribution, and scores above this value account for half of the remaining 32% of the distribution beyond one standard deviation.

Step-by-step explanation:

To solve for the percentage of students who scored more than 65 marks, we use the properties of the normal distribution. Given that the mean score is 60 and the standard deviation is 5, a score of 65 is one standard deviation above the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean (between 55 and 65 in this case), meaning 34% falls on each side within this range. Scores beyond one standard deviation above the mean (greater than 65) account for half of the remaining percentage, which is half of 32% (100% - 68%) or 16%. Therefore, the percentage of students who scored more than 65 marks would be 16%.