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?

Question

Manuel Jackson

Mathematics

11 December, 15:03

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?

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Caitlin Bowers · Answer 1

84%

Step-by-step 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%.