1. THE STANDARD NORMAL DISTRIBUTION
SECTION 6.2
THE STANDARD NORMAL DISTRIBUTION

2. NORMAL PROBABILITY DISTRIBUTION
The mean, median and mode are the same.
The distribution is bell-shaped and symmetrical around the mean.
The total area under the curve is equal to 1.
The left side and the right side of the normal probability distribution extend indefinitely, never quite touching the horizontal axis.

3. NORMAL DISTRIBUTION
If a continuous random variable has a distribution with a graph that is symmetric and bell-shaped and it can be described by the equation we say that is has a normal distribution.

4. STANDARD NORMAL DISTRIBUTION
Is a normal distribution with the parameters of µ = 0 and σ = 1. The total area under its density curve is equal to 1.

5. FINDING PROBABILITIES
This section will have you find the probability / area under the curve to the z – score.
There are 5 unique style questions
P(a < z < b)
P(a < z )
P(z < b) Zα P%

6. P(a < z < b)
The probability that the z score is between a and b.

7. P(a < z)
The probability that the z score is greater than a.

8. P(z < b)
The probability that the z score is less than b. b

9. Zα
The z-score with an area of α to its right.

10. P% The z-score with an area from 0 to the given %.
Change % to decimal, % = α .

11. Calculator – Inequality
How to find the probability with a TI
Go to folder DISTR (2nd Vars)
Press 2 (normalcdf) – gives percentage of area under a standard normal distribution.
Normalcdf(lower bound, upper bound) OR
Normalcdf( lower bound, upper bound, mean , standard deviation)

12. TABLE - Inequality
Given the z score table the graph at the top of the page shows you the probability / area. Understand different z scores shade different sides, so be careful.
The probabilities / areas are on the inside.
The z – score is broken up into two parts
The whole and the tenth number are on the side
The hundredth number is on the top
Match the two together to find the prob / area

13. EXAMPLE
Find the probability of a normal standard deviation between and 1.78

14. EXAMPLE
Find the probability of a normal standard deviation greater than -1.04

15. EXAMPLE
Find the probability of a normal standard deviation less than -1.04

16. Calculator - Zα Subtract : 1 – α Distr (2nd vars) InvNorm(
Type in 1 – α
enter

17. Table - Zα Look at the shaded region of the z table
This α connects with a shaded region to the right, if you need the shaded region to the left then subtract from 1, 1 – α
Find the value inside the z score table
Look up and to the left and find the z value

18. EXAMPLE
Evaluate z0.025

19. Calculator - P% Distr button (2nd vars) Press number 3 invNorm
InvNorm (area → decimal no %)

20. Table - P% Look at the middle section of the z score table
Convert & to decimal
Find the probability
If exact probability is not there adjust accordingly
Move up and left for the two part and combine them.

21. EXAMPLE
Evaluate P90

22. EXAMPLE
Evaluate z0.025