Question

If students’ scores were normally distributed and the mean was 200 with a standard deviation of 40, then what is the probability, in percentages, that it is below 240?

Answer 1

84%

Explanation:

The empirical rule tells you that 68% of the standard normal distribution is within 1 standard deviation of the mean. The distribution is symmetrical, so the amount in the lower tail is (1 -68%)/2 = 16%.

Since the number you're interested in, 240, is one standard deviation above the mean (200 +40), the percentage of interest is the sum of the area of the central part of the distribution along with the lower tail:

68% + 16% = 84%.