BINOMIAL PROBABILITY DISTRIBUTION
PICK UP A NOTES SHEET FROM THE
FRONT TABLE!
In a binomial experiment,
There are TWO mutually exclusive outcomes, often referred to
as “success” and “failure”. If the probability of success is p, the
probability of failure is 1 – p.
In a binomial experiment, we can compute probabilities of certain
outcomes.
For a binomial experiment to occur, these four conditions must be met:
1. There are a fixed number of observations (n).
2. Each observation is independent.
-
3.
Each observation falls into only TWO categories: success and failure.
-
4.
Ex: In a situation where tossing a coin, the 5th toss is not dependent on any of the
previous 4 tosses. They are independent!
Probability of success is labeled p
Probability of failure is labeled 1-p
The probability of success, p, is the same for each of the n observations.
The probability of an event, p, occurring exactly r times:
In the calculator: binompdf(n,p,r)
Note: r refers to some number of successes between 0 and n.
2nd Vars: A:binompdf(n, p, r)
n = # of trials
p = probability of success
r = # of specific events you wish to obtain (may also be called x)
#1
Eight out of every 10 persons who contract a certain viral infection can
recover. If a group of 9 people become infected, what is the probability that
exactly 5 people will recover?
#2
In Lisa’s art class, 1 out of 5 paintings that she makes will be chosen for an art show. If
she is preparing 9 paintings for the competition, what is the probability that exactly 2
of them will be chosen?
Math III
Warm Up
4/30/14
1. If Jim Bob makes a 35 on his Spanish test with a mean of 30
and a standard deviation of 2, did he do better that Dixie who
made a 76 on her English exam with a mean of 74 and a
standard deviation of 3?
2. 2 out of fifteen students fail a class their freshman year. What
is the probability that out of a group of 10, exactly 3 freshmen
will fail a class?
#3
Assume that 60% of marigold seeds that are sown directly in the ground
produce plants. If Big Bird plants 10 seeds, what is the probability that
a) at least 7 plants will grow?
b) at most 2 plants will grow?
In the calculator: For any situation other than P(x = r),
use 2nd Vars: B: binomcdf(
• To find P(x ≤ r), use binomcdf(n, p, r)
• To find P(x < r), use binomcdf(n, p, r – 1)
• To find P(x > r), use 1-binomcdf(n, p, r)
• To find P(x ≥ r), use 1-binomcdf(n, p, r – 1)
• Note: r refers to some number of successes between 0
and n.
Mean and Standard Deviation of a Binomial Distribution
Formulas:
Mean: 𝜇 = 𝑛 ∙ 𝑝
Standard Deviation: σ = 𝑛 ∙ 𝑝(1 − 𝑝) = 𝜇 ∙ (1 − 𝑝)
A basketball player has a free throw percentage of 75%. In a single game, the
player shoots 12 free throws. Find the mean and standard deviation for this
player.