Question

A group of 200 students took a test. The mean was 80, the standard deviation was 7 and the scores were normally distibuted. Approxmately how many scores would fall between 80 and 87?

A. 136

B. 68

C. 100

D. Impossible to determine

Answer 1

The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, provides a quick estimate of the spread of data in a normal distribution given the mean and standard deviation. Specifically, the empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.
95% of the data will fall within two standard deviations of the mean.
Almost all (99.7%) of the data will fall within three standard deviations of the mean.

Here 80 and 87 represents the area between 0 and 1

Hence 34% lies.

Scores that lies between 80 and 87 are 200*0.34 = 68

Ans: 68 (Option B)