Students pass a test if they score 50% or more.

The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.

Assuming this data is normally distributed, what percentage of students pass the test?

Question

Students pass a test if they score 50% or more.

The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.

Assuming this data is normally distributed, what percentage of students pass the test?

vshiroky · Answer

@agent0smith

agent0smith · Answer

the mean and standard deviation were calculated as 42% and 8% respectively. Which means that 50% is exactly one standard deviation away from the mean. https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/2000px-Standard_deviation_diagram.svg.png You want to add up the percentages from this graph that are to the right of $\large 1\sigma$.