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.