Question

The time required to finish a test in normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. What is the probability that a student chosen at random will finish the test in more than 56 minutes?


84%

2%

34%

16%

Answer 1

This is the bell curve. The first SD means that about 68% of the students are expected to score between 32 and 48 points (40 plus/minus 8).

The second SD means that an additional eight points gets added/subtracted. That means that about 95% of the students should score between 24 and 56 points.

The third SD means that an additional eight points gets added or subtracted. That means that about 99.7% of the students should score between 16 and 64 points.

Your question asks about the percentage of students that should score more than 56 points. You want to know that percentage accounted for up to 56 points. Since 95% should fall between 24 and 56 points, that means 5% are unaccounted for: they get the lowest and highest scores. We don't care about the lower scores (the lower 2.5%), we care about the higher scores (the higher 2.5%). Your answer is this: about 2.5% of the students should score above 56 points on the test.

Answer 2

so it would be 2 percent.

Answer 3

yes :)