Download Binomial and Geometric Formulas

BINOMIAL vs. GEOMETRIC DISTRIBUTIONS
ASSUMPTIONS
DESCRIPTION
FORMULA
TI instructions
Discrete BINOMIAL
1. 2 outcomes: “success” & not
“success”
2. Independent trials
3. P(“success”) is constant
4. Number of trails is fixed
B(n, p)
P(X = k)= n Ck pkqn-k
where:
n = # of trials
k = # of “successes”
p = probability of “success”
q = probability of not “success”
binompdf (n, p, X)
binomcdf (n, p, X)
Discrete GEOMETRIC
1. 2 outcomes: “success” & not
“success”
2. Independent trials
3. P(“success”) is constant
4. X is the 1st trial
G(p)
Example: What is the
probability that I will get 3 Lady
Gaga’s (p = 0.2) out of 10 boxes?
Example: What is the probability that I
will get my first Lady Gaga (p = 0.2) on
the 3rd or 4th box?
Answer: 1 – binomcdf(10, .2, 3)
Or,
C4 (.2 4 )(.86 )+ 10 C5 (.2 5 )(.85 )
10
Answer:geometpdf(.2,3)+geometpdf(.2,4)
Or,
P(X is 1st)= q x-1p
where X is the Xth
geometpdf (p, X)
geometcdf (p, X)
(.82 )(.2)+(.83 )(.2)
+...+ 10 C10 (.210 )(.80 )
NORMAL APPROXIMATION OF BINOMIAL & GEOMETRIC* DISTRIBUTIONS
ASSUMPTIONS
Continuous BINOMIAL
1. np ³ 10 and nq ³10
2.
DESCRIPTION
FORMULA
N(m,s)
m = np
Continuous GEOMETRIC
Normal approximation NOT used
because geometric distribution is
skewed
m= 1
p
s = npq
x -m
s
Normcdf(lower, upper)
s=
q
z=
TI instructions
* Normal approximation of geometric not included in AP Statistics.
p2