You recently took a statistics exam in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 8, but when you talk to other students in the class, you find out that more than 30 students have scores below 45. That violates which rule for the Normal distribution?
A)the 1-2-3 rule
B)the 30-60-90 rule
C)the 68-95-99.7 rule
D)It does not violate any rule; anything can happen.

Question

Quizplus · Accepted Answer

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. Given the mean score is 72 and the standard deviation is 8, a score of 45 is more than three standard deviations away from the mean (72 - 3*8 = 48). Therefore, having more than 30 students score below 45 is highly unlikely in a normal distribution, indicating a violation of the 68-95-99.7 rule.

You Recently Took a Statistics Exam in a Large Class