Transcript 4.2 Binomial Distributions

4.2 Binomial Distributions
I.
•
Binomial Experiments
A binomial experiment is a probability
experiment that satifies the following conditions:
1. Fixed number of independent trials
2. Only 2 possible outcomes: success/failure
3. P(s) is the same for each trial
4. The random variable x counts the number of
successful trials
• Notation
n
the # of times a trial is repeated
p = P(s)
the probability of success in a
single trial
q = P(f)
q = 1 – p ; probability of failure
x
the number of successes in n
trials
II. Binomial Probability Formula
• In a binomial experiment, the probability of
exactly x successes in n trials is:
P(x) = nCx ∙ px ∙ qn-x
• Now read example 2 (p186) and complete TIY#2
HW: p194-195
#6, 8, 14a, 20a, 22a
• Binomial Probability Distribution: the list of
all possible values of x with the
corresponding probability of each
• Read example 3 (p187) and complete TIY#3.
III. Finding Binomial Probabilities
• There is a way to do
this on your TI-83+
calculator!
– Press 2nd VARS to get
to your distribution
menu; scroll down to
0:binompdf(
– Then you enter n, p, x)
P188 Do example 4
& TIY#4
Now how is example 5 different?
• At least or less than problems use a
different command in the calculator.
• In the DIST menu select A:binomcdf(n, p,
x) This will add up all probabilities starting
with 0 and ending at x.
• Do example 5 and TIY#5
There is a table….will you use it???
IV. Graphing Binomial Probabilities
I.
Same process as a discrete probability
distribution
Example 7 p191
Now do TIY#7
on a piece of graph paper and submit.
Graphing binomial distributions
continues….
• Skewed left: p> 0.5
• Skewed right: p< 0.5
• Symmetric: p = 0.5
HW: p193-195
#2, 4, 14b&c, 20b&c, 22b&c
V.
Mean, Variance, and
Standard Deviation
• The formulas are much simpler for a
binomial distribution
• Mean: μ = n•p
• Variance: σ2 = n•p•q
• Standard deviation: σ = √ n•p•q
• P192 Example 8 & TIY#8
HW: p194-195
#10, 12, 16, 18, 20d,e,f,
22d,e,f