1. f(x) x Figure 1 g(z) z Normal distribution for Cholesterol with.4
Normal distribution for
Cholesterol with
Mean = 219 and SD = 50 .3
f(x) .2 .1 19 69
119
169
219
269
319
369
419 x
200 on N(219, 2500)
Maps into on N(0,1)
Standard normal distribution
i.e. mean = 0 and SD = 1 .4 .3
g(z) .2 .1 -1 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 11 12 13 z

2. Normal distribution with
Figure 2
Normal distribution with
Mean = 5 and SD = 2 .4 .3
f(x) .2 .1 -3 -1 1 3 5 7 9 11 13 x .4 .3
g(z)
8 is one and a half SD’s (SD = 2)
above the mean 5, so 8 maps into
1.5 which is one and a half
SD’s (SD = 1) above mean 0. .2 .1 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13

3. Normal distribution for Cholesterol
Figure 3
Normal distribution for Cholesterol
Mean = 219 and SD = 50
N(219,2500) = N(219,502) .4 .3
f(x) .2 .1 19 69
119
169
219
269
319
369
419 x
35% of area
under curve
200 .4 .3
. di ( )/50
-.38
. di normal(-0.38)
. di normal(( )/50) .2 .1 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-0.38
Standard Normal Distribution Mean = 0 and SD = 1

4. f(x) x Figure 4 35% of area under curve
N(219,2500) = N(219,502) .4 .3
f(x) .2 .1 19 69
119
169
219
269
319
369
419 x
35% of area
under curve
200 .4 .3 .2
. di invnormal( ) .1 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-0.38
Standard Normal Distribution Mean = 0 and SD = 1