6. The Normal Distribution

j. explain the key properties of the normal distribution;

What is a normal distribution?
It is a symmetrical distribution with a bell curved shape.

How do the mean, median, and mode describe the normal distribution?
They are all the same.

What is a point estimate?
Sample mean and sample deviation are called point estimates.

What is a confidence interval?
Confidence intervals use point estimates to make probability statements about the dispersion of the outcomes of a normal distribution. A confidence interval specifies the percentage of all observations that fall in a particular interval.

What are the formulas for 90/95/99% confidence intervals?
- 90% $$-1.645 \sigma <= \bar{x} <= 1.645 \sigma$$
- 95% $$-1.96 \sigma <= \bar{x} <= 1.96 \sigma$$
- 99% $$-2.58 \sigma <= \bar{x} <= 2.58 \sigma$$

Source:

• CFA