1. Normal Distribution Objectives: (Chapter 7, DeCoursey)
To define the Normal distribution, its shape, and its probability function
To define the variable Z, which represents the number of standard deviations between any point x and the mean μ.
To demonstrate the use of Normal probability Tables and Excel functions for solving Normal distribution problems.

2. Normal Distribution Symmetrical Shaped like a “bell”
Mean, median and mode coincide
Sometimes referred to as the Gaussian distribution.

3. Normal Distribution Probability function for the Normal distribution:
μ: specifies the location of the center of the distribution; σ: : specifies the spread.

4. Normal Distribution a b
Probability that a continuous random variable that obeys the Normal distribution lies within the limits “a” and “b”:

5. Normal Distribution
Only numerical solution is available (Normal Distribution Tables).
Challenges: an infinite number of probability distributions exist for various values of μ and σ, which leads to an infinite number of tables.
Solution: A single curve is obtained by a simple change of variable:
z: the number of standard deviations between any point x
and the mean,μ.

6. Standardized Normal Distribution
f(z) z

7. Cumulative Normal Distribution
Φ(Z) Z Z