Lesson Five: Normal Distributions

Question 1

Normal Distribution or Normal Density Curve:

Answer 1

A common way data is shown in a graph. Here’s some properties of normal distributions:

-Symmetric bell shape

-The total area under the curve equals one.

-The density curve always lies on or above the horizontal axis.

-Mean and median are both equal, both located at the center of the distribution

-About 68% of the data falls within 1 standard deviation of the mean

-About 95% of the data falls within 2 standard deviations of the mean

-About 99.7% of the data falls within 3 standard deviations of the mean

-This is also called a Gaussian distribution after Carl Friedrich Gauss.

-The area under the curve can be treated as a probability.

-A normal density curve is uniquely determined by its mean, u, and its standard deviation, o.

Question 2

Standard Normal Distribution:

Answer 2

When the mean of a normal distribution is zero and its standard deviation is one.

Question 3

Z-Scores:

Answer 3

The measurement of how many standard deviations from the mean the observation lies.

Formula: z = (x - u ) / o

z= z score
x= observation point
u= mean
o= standard deviation

Question 4

The Empirical Rule or 68-95-99.7 Rule for Bell shaped Distributions:

Answer 4

For any bell shaped distribution, the following is true:

-About 68% of the data falls within 1 standard deviation of the mean

-About 95% of the data falls within 2 standard deviations of the mean

-About 99.7% of the data falls within 3 standard deviations of the mean

Question 5

Unusual Observation:

Answer 5

If a z-score is extreme (either positive or negative), that suggests the observed value is very far from the mean. This is when something happens less than 5% of the time. If z is greater than 2 or less than negative 2, it’s an unusual observation.

Question 6

Normal Probability Applet:

Answer 6

An interactive normal distribution that helps us find proportions and probabilities from the z-score.