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%).