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% \(-2.58 \sigma <= \bar{x} <= 2.58 \sigma\)