Students pass a test it 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% respectivley. assuming this data is normally distributed, what percentage of students pass the test

So we are given that the mean is 42% and the sd (standard deviation) is 8%
Assuming our data is normal we can use the 68-95-99 rule

So one thing you should realize is that 42% + 8% is 50% which is passing. That is one standard deviation higher. So we use:
 
100 - 68 - 13.5 - 2.35 - 0.15  = 16. That means 16% of students passed the test. Which is terrible. They probably need to hit the books more.

Anyways if you have any question feel free to message me!
Hopes this helps!

What do you mean by that?