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.

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Hopes this helps!

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