Download B(n, p)

AP Statistics
8.1 The Binomial Distribution
The Binomial Setting – Must have these four characteristics
1. Each observation falls into one of ONLY two categories; SUCCESS or FAILURE
2. There is a fixed number n of observations
3. The n observations are all independent. Knowing the result of one observation tells
you nothing about the other observations.
4. The probability of success, p, is the same for observations.
The Binomial Random Variable
X=
Binomial Distribution –
B(n, p)
Example 8.1 (pg. 516)
Exercise 8.2 (pg. 516)
Binomial Distribution in the Statistical Sampling

Exercise 8.6 (pg. 516)
Binomial Coefficient
n=
k=
REMEMBER:
Binomial Probability
If X has binomial distribution with n observations and probability p of success on each
observation, the possible values of X are 0, 1, 2, …, n. If k is any of these values,
Example 8.7 (pg.519)
Example 8.8 (pg.519)
Find Binomial Probabilities
pdf: Given a discrete random variable, the Probability Distribution Function (PDF) assigns
a probability to a specific value of X. P(X=value)
On the calculator: binomialpdf(n,p,k)
cdf: Given a discrete random variable, the Cumulative Distribution Function (CDF) is the
sum of p for 0, 1, 2, 3,…, X. Think a range, P(X ≤ values)
On the calculator: binomialcdf(n,p,{k})
NOTE: k is the LAST VALUE
Revisit examples 8.7 and 8.8
Example 8.13 (pg.516)
X
pdf
cdf
1
2
3
4
5
Mean and Standard Deviation of a Binomial Random Variable
Normal Approximation to a Binomial Distribution
Suppose that a count X has the binomial distribution with n trials and probability of success p.
When n is large, the distribution of X is approximately Normal,
. As a rule of
thumb, we can use a Normal approximation if np ≥ 10 and n(1 – p) ≥ 10.
Exercise 8.19
HW: pg. 523; 8.3, 8.4, 8.14, 8.16, 8.18, 8.32, 8.34, 8.38