1. Normal Distribution Standardising Scores & Reverse
Stats 1 with Liz

2. Starter
Given that
Find
(a)
(b)
(c)
General Rule:

3. P(Z > -0.6) has the same area as P(Z < 0.6).
z is a Negative Value
Example 1: Find P(Z > -0.6).
Looking in your chart, there are no negative values listed…
To get around this, simply make a quick sketch of the normal distribution curve & find a symmetrical point that is in the table.
P(Z > -0.6) has the same area as P(Z < 0.6).
P(Z < 0.6) =

4. z is a Negative Value
In general: If we are looking for a negative z value, we can find it in the table by looking for the same positive value, but the inequality sign has flipped!

5. z is a Negative Value Example 2: Find P(Z < -1.4).
Look at a sketch & use the new flip rule.
This is the same as P(Z > 1.4).
Remember, our table only tells us values LESS THAN z, so we need to work out 1 – P(Z < 1.4).
1 – P(Z < 1.4) = 1 – =

6. z is a Negative Value
For the situation on example 2, you can either think through the process, or simply memorise the shortcut:

7. z is Between Two Values
General Rule: If z is between two values, such as
P(a < Z < b)…
It is the same as finding P(Z < b) – P(Z < a)

8. z is Between Two Values Example 3: Find P (1.0 < Z < 2.0)

9. Working backwards
Sometimes the question will give you the probability and ask you which z value it works for.
Example 4: Find z when
To work this out, look in the table to find the closest z value that yields as its probability.
z is 2.6.

10. Working backwards
Example 5: Find
(a) (b)

11. What if our mean isn’t 0 and variance isn’t 1?
In this case, we have to standardise our score using this formula:

12. Standardising Scores
Example 6:

13. You try!

14. Solutions

15. Solutions

16. Solutions

17. Solutions
HINT:

18. Independent Study