Question

This is a graded discussion: 10 points possible due Oct 6 The Normal Distribution Answer one of the following questions: Why do we use a bell curve to assess the normality of a variable as opposed to a square, triangle, or some other symmetrical shape? Imagine that you recently took a statistics exam and your instructor just returned your graded exam. The instructor announces that 75% of students scored below the mean. How do you reconcile this with the fact that, in a normal distribution, half the scores should fall below the mean and half of the scores should fall above the mean? Make sure you reply to another student for full credit Search entries or author Unread

Answer 1

A bell curve is the most common type of distribution for a variable and is thus considered to be a normal distribution. The important thing to note about a normal distribution is the curve is concentrated in the center and decreases on either side, the bell shape curve exactly fits the description of being concentrated at the mean

A normal curve or a bell curve is important in statistics because it can model a wide variety of real-world data. While some other symmetric shapes like a rectangle, triangle would not be a good fit for normally distributed data which depends on the standard deviations of the data.

Average Person Most People Some People Some People

As the distance from mean increases, the values get rare.

The instructor's statement " 75% of the people scored less than mean " such a case is possible but in this case the curve will not be a perfectly symmetrical bell curve, It would rather be skewed to the right(positive skew), which means median < mean.

The curve would look something like this.

Median Mean Positive skew