1. APPLICATIONS OF THE NORMAL DISTRIBUTION

2. EXAMPLE 1
IQ intelligence scores have a mean of 100 and a standard deviation of 15. If one person is selected at random, what is the probability he will have an IQ
a) greater than 115?
b) less than 95?

3. Example 1 – answer a
First, find the z-score corresponding to the raw score of 115
Determine the shaded region.
Determine proper area from chart. 1 1
Subtract from .5 because tail section:
Final answer : A = or 15.87%
From chart: A= .3413

4. Example 1 – answer b Determine the shaded region.
Determine proper area from chart.
-.33
Subtract from .5 because tail section:
Final answer : A = or 37.07%
From chart: A= .1293

5. Example 2
The lengths of sardines have a mean of 4.64 inches and a standard deviation of .25 inches. If the distribution is normal, what percentage of these sardines are
a) shorter than 5 inches?
b) from 4.4 to 4.8 inches long?

6. Example 2 - answer Determine the shaded region.
Determine proper area from chart.
1.44
Add .5 because greater than the mean:
Final answer : A = or 92.51%
From chart: A= .4251

7. Example 2 – answer b Determine the shaded region.
Determine proper area from chart.
-.96
.64
Add together because on opposite sides
of the mean :
Final answer : A = or 57.04%
From chart: A= .2389
A= .3315

8. FINDING A CUT-OFF SCORE
Modified z-score formula for finding a raw- score or cut-off score

9. Example 1:
A special enrichment program in mathematics is to be offered to the top 12% of students in a school district. A standard math test given to all students has a mean of 57.3 and a standard deviation of Find the cut-off score for the program.

10. Example 2:
An exclusive college desires to accept candidates who score in the 90th percentile or above based on a national placement test. This test has a mean of 500 and a standard deviation of Find the cut-off score.

11. Example 3:
For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure. If the mean blood pressure is 120 and the standard deviation is 8, find the upper and lower readings that would qualify people to participate.