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Transcript
The Binomial
Distribution
Introduction
#
correct
Tally
Frequency
P(experiment)
P(theory)
0
1
2
3
Mix the cards, select one & guess the type. Repeat
3 times per turn and record your results.
Introduction
# correct
Tally
Frequency P(experiment)
P(theory)
0
1
2
3
4
Repeat guessing 4 times – Graph the results
Binomial Formula for theory
P(X =x) = nCx x(1 - )n-x
• Where n is the number of trials.
•  is the probability of success.
Definition of the Binomial Distribution
The Binomial Distribution occurs when:
(a) There is a fixed number (n) of trials.
(b) The result of any trial can be classified as a “success” or a “failure”
(c) The probability of a success ( or p) is constant from trial to trial.
(d) Trials are independent.
If X represents the number of successes then: P(X =x) =
nC
x
x(1 - )n-x
PARAMETERS of binomial distribution
Parameters = what describes the distribution
‘n’ Fixed number of trials.
‘’ or ‘p’ The probability of a success.
Example #1
a) Flipping a coin 8 times – what is the
probability that exactly 3 of them are heads?
b) Does this experiment meet the conditions of a
binomial distribution?
Example #2
Calculate the probability of a drawing pin landing on its back 3
times in 5 trials if the probability of getting a drawing pin to land on
its back on any toss is 0.4
Let X be a random variable representing the number of “backs” in 5
tosses of the drawing pin. Then X is binomial with n = 5,  = 0.4.
We want P(X = 3).
(i) By formula: P(X = 3) =
(ii) Using tables: P(X = 3)
5C
3
× 0.43 × 0.62
= 0.2304