FRAME 70.
The z equation can be manipulated algebraically. Since a and b are the values of interest, we will
use them instead of X:
Below the Mean
Above the Mean
1.
-z= a-u
z= a b-u
σ
σ
- zσ = a- u
zσ= b - u
2.
Multiply both
sides by σ
u- zσ= a
u+ zσ= b
3.
Add u to both
sides.
As before, -z is used to denote standard deviations below the mean, and z is used to denote
standard deviations above the mean.
We know 3 of the values in equation 3: u = 175, z = 1.29, and σ = 6. Given this information
we can compute a and b.
a= u- zσ
b= u+ zσ
a = 175 - (1.29) (6)
b = 175 + (1.29) (6)
a = 175 - 7.74
b = 175. + 7.74
a = 167.26
b = 182.74
Thus, we can say that the middle 80% of the recruits have heights between 167.26cm and
182.74cm.
The middle 95% of all trainees could be expected to have heights between what two values? Use
the table of areas under the normal curve to find the values. Draw the diagram.
103
FI0921
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