Probability Formula Review Page 2
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2V. The continuous normal probability distribution
A. To findthe probabilityof x being withina given range:
B. To find a
range for x given the probability: J..l::!: Z(J
VI. Central limit theorem
P(x)
Sampling
Distribution
of the Means
~
J..l
J..lx
If
n;;::
30, the population may be skewed.
x
VII.Point estimates
A.
x
for f..l
B.
c.
p forp
s for 0"
VIILlnterval estimates
when n ;;::30
A. For a population mean
0-
XIZJii
5
XIZJii
or
-
JP(1-P)
B. For a population proportion
p + z ~
where
IX. Determining sample size
A. When estimating the population mean
n
= (z;)2
X-f..L
Z=cr-
Normal approximation of the binomial
requires
n;;::
30and both np and nq are;;::5.
The continuity correction factor applies.
D.
Sxforo"xwhere Sx=!n and o"x = In
x
p
=fj
B. When estimating the population proportion
n=p(1-p>(~)2
77
Note: Use the finite
correction
factor in section VIII formulas
when n/N;?:.05.
J
N-n
N-1
Section VIII
Note: Whenn < 30 and
0" is unknown, the t distribution, to
be discussed in chapter
16, must be
substituted for the z distribution when
making interval estimates. Many
statistics software programs do all
interval calculations, regardless of
sample size, using the t distribution.
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