S05
Statistics 305A
Using Table B.3 to Find Approximate CDF Values p and
Quantiles xp in Normal Populations
The relationship between same p-value quantiles in N(0, 1) and N(µ, σ 2) is given in Handout 4a
as
xp = µ +σ zp .
(1)
Values of the CDF of the N(0, 1) population (p-values) are given in the body of Table B.3.
Quantile values zp are given in the left and top margins. This Table, along with relationship (1)
can be used to obtain p-values and p-quantiles in N(µ, σ 2) for given µ and σ 2.
1. To find xp for given p, find zp from Table B.3 (as close as you can without interpolating
between tabled p-values) and evaluate (1) above.
2. To find p-value given xp, compute zp = (xp − µ)/σ and find the CDF of N(0, 1) at zp from
Table B.3 (as close as you can without interpolating).
Exercises
1. Find xp given µ, σ 2, and p.
µ
2
10
−2
0
−5
σ2
9
1
4
25
0.5
p-value
0.8365
0.0013
0.6700
0.9850
0.1190
xp
2. Find the CDF value p, given µ, σ 2, and xp.
µ
2
10
−2
0
−5
σ2
9
1
4
25
0.5
xp
4
8
0
5
−4.5
CDF value p