Question

(Please answer the question in its entirety

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

Solution:-

Mean = 76, S.D = 5

The percent of students in the class scored between 66% and 86% on the exam is 0.954.

x₁ = 66

x₂ = 86

By applying normal distribution:-

z₁ = -2.0

z₂ = 2.0

P( -2.0 < z < 2.0) = P(z > -2.0) - P(z > 2.0)

P( -2.0 < z < 2.0) = 0.977 - 0.023

P( -2.0 < z < 2.0) = 0.954

One standard deviation means the data points is at a distance of 1 standard deviation below or above the mean.

Two standard deviation means the data points is at a distance of 2 standard deviation below or above the mean.