FRAME 69.

Often we know the area under the curve and want to find the associated values on the

horizontal base line. For example, the middle 80% of all trainees could be expected to have

heights between what two values? Unless otherwise specified, it is assumed the given area is

centered on the mean. A diagram would appear as follows:

u = 175

The shaded area is 801 (in this case) of the total area and the distance from a to 175cm is the

same as the distance from 175cm to b. We want to find values for a and b. By symmetry, the

shaded area on each side of the mean is 40% (half of 80%). Recall the construction of the table

of areas under the normal curve. The perimeter values give standard deviations and the body of

the table gives areas. In this case, we will work in the opposite direction. Instead of knowing

standard deviations and looking up the corresponding area, we will know the area and look up

the corresponding standard deviation. In our example, we will look up an area of .4000. From the

table we see that no entry is exactly .4000. We will use the higher z value if the area (%) falls

between two areas (%) on the table. For an area of .4000, the z value would be 1.29.

Initial Area

Lower Area (A)

Higher Area (%)

Value

__ Value__

__ and Value__

__ and Value__

Selected

.4500

.4495

.4505

1.64

1.65

1.65

.4000

.3997

.4015

1.28

1.29

1.29

.3400

.3389

.3413

.99

1.00

1.00

.2500

.2486

.2518

.67

68

.68

.2075

.2054

.2088

.54

55

.55