The mean of normally distributed test scores is 82 and the standard deviation is 2. If there are 224 test scores in the data sample, how many of them were in the 76 to 78 range?

Question

The options are 30, 6, 106, and 76. Please help ASAP, I am having trouble with this. Thank you.

Answer 1

The answer is 6.

You can use the empirical rule of normally distributed data. The proportion of data between range 76 to 78 is the proportion between 2 standard deviation and 3 standard deviation below the mean. That proportion is 2.35 percent according to the empirical rule.

2.35 percent of the sample size, 224, is 5.264 ≈ 6 when rounded up.