Question

The distribution under the normal curve can be seen a lot in society, although you may not even notice it. Have you been watching the presidential candidate polls on tv? If you ever see the +- 3 that is beside the percentage given on if they are winning; that is the standard deviation. This is exactly what they are referring to. So really, how accurate are those polls?

Now, here's another example to discuss in this week's post. If we say that the average on the first exam was a 76% with a standard deviation of +-5%. What percent of students in the class scored between 66% and 86% on the exam? (What is one standard deviation? What is two standard deviations?) How did you come up with this? Explain.

Answer 1

By Empirical Rule:

For a Normal Distribution, 68% of data will fall within one standard deviation from themean

95% fall within two standard deviation from mean

99.7 % fall within three standard deviation from mean.

Given Example:

Average score on exam = 76% with standard deviation +-5%.

Thus, we have:

Mean = 76%

one standard deviation = 5%

two standard deviation = 2 X 5% = 10%

So,

between 66% and 86% is same as mean two standard deviation.

By empirical rule:

95% of data fall within two standard deviation from mean.

Thus, the answer is:

95% of students in the class scored between 66% and 86% on the exam.