Normal Distribution Concepts and Properties

The video tutorial explains the normal distribution, also known as the Gaussian or Bell Curve, highlighting its symmetrical nature where mean, median, and mode are equal. It covers the notation used for normal distribution and how the graph's highest point aligns with the mean. The tutorial further explores how changes in mean and standard deviation affect the distribution's position and shape, using histograms as examples. The lesson concludes with a preview of the next topic on standardization.

What is another name for the normal distribution?

• Poisson distribution

• Bell Curve

• Uniform distribution

• Exponential distribution

In a normal distribution, which of the following are equal?

• Mode and variance

• Median and standard deviation

• Mean, median, and mode

• Mean and variance

What does the tilde sign in the notation of a normal distribution represent?

• It represents a function

• It indicates a variable

• It denotes a distribution

• It shows a constant

What determines the spread of a normal distribution graph?

• Standard deviation

• Mode

• Mean

• Median

In a normally distributed histogram, where are most observations concentrated?

• At the tails

• At the mode

• Around the mean

• At the origin

What happens to the distribution when the mean is increased, keeping the standard deviation constant?

• The graph moves to the left

• The graph moves to the right

• The graph becomes wider

• The graph becomes taller

How does a lower standard deviation affect the shape of the distribution?

• It results in a wider distribution

• It results in fatter tails

• It results in a taller distribution

• It results in a lower dispersion

What is the effect of a higher standard deviation on the distribution?

• The graph becomes narrower

• The graph flattens out

• The graph moves to the left

• The graph becomes taller

What is the result of controlling for the mean while changing the standard deviation?

• The graph moves left or right

• The graph remains unchanged

• The graph reshapes

• The graph becomes symmetrical

What is the statistical term for the tails of a distribution?

• Thin tails

• Fat tails

• Short tails

• Long tails