1. Finding z-scores using Chart

2. OBJECTIVE
Find the z-score of a standard normal distribution.

3. RELEVANCE
Find probabilities and values of populations whose data can be represented with a normal distribution.

4. Sometimes, you must find a specific z-value for a given area under the curve. The procedure is to work backward.

5. Example…….
Find the z-score such that the area under the normal distribution curve between 0 and z is
Draw and Shade.
Find the area closest to in the chart and work backwards.
Answer: z=0.56

6. Example…… Find the z for an area of .4066 between 0 and z. Answer:

7. Example…… Find the z for an area of .0239 to the right of z.
First find the area between 0 and z: =
Next, find the z-score closest to
Answer: z=1.98

8. Example…… Find the z for an area of 0.9671 to the left of z.
First, find the area between 0 and z:
– =
Next, find the z closest to
Answer: z = 1.84

9. Example…… Find the z-value to the right of the mean so that
a % of the area lies to the left of it.
b % of the area lies to the left of it.

10. Answer…… 53.98% to the left. Area needed: 0.5398 – 0.5000 = 0.0398.
z-score = 0.10

11. 71.90% to the left.
Area needed: – =
Answer: z = 0.58

12. Example…… Find the z-score for an area of 0.05 to the right of the z.
NOTE: If an area is exactly in between 2 areas, use the larger z-score.
Area needed:
– =
Answer:
Z = 1.65

13. Example……
Find the z-scores for an area of 40% that falls between two z-scores.
Area needed:
0.4000/2 =
Answer:
z = and +0.52