Pre-Lecture 9 Normal Distribution

What is a standard​ score? How do you find the standard score for a particular data​ value?

A standard score is the number of standard deviations a data value lies above or below the mean.

When referring to a​ "normal" distribution, does the word normal have the same meaning as it does in ordinary​ usage? Explain.

The word normal has a special meaning in statistics. It refers to a specific category of distributions that are symmetric and​ bell-shaped with a single peak. The peak corresponds to the​ mean, median, and mode of such a distribution.

In a normal​ distribution, approximately​ 68% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

one

In a normal​ distribution, approximately​ 99.7% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

three

In a normal​ distribution, approximately​ 95% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

two

Identify which of the following is not a property of the Normal probability density function or state that they all are.

A Normal curve will have a single​ peak, in the​ middle, which occurs at a value equal to the​ mean, median, and mode of the distribution.

What does the area under the normal distribution curve​ represent? What is the total area under the normal distribution​ curve?

The area that lies under the normal distribution curve corresponding to a range of values on the horizontal axis is the total relative frequency of those values. Because the total relative frequency for all values must be 1​ (100%), the total area under the normal distribution curve must equal 1​ (100%).