6.2 binomial probability distribution objectives: by the end of this section, i will be able to…...
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6.2 Binomial Probability DistributionObjectives:By the end of this section, I will beable to…
1) Explain what constitutes a binomial experiment.
2) Compute probabilities using the binomial probability formula.
3) Find probabilities using the binomial tables.4) Calculate and interpret the mean, variance,
and standard deviation of the binomial random variable.
LifeThere are many times in life when
there are only two possible outcomes.
A baby is about to be born. Boy or Girl?
Basketball player is fouled. Make or miss?
You are about to ask a girl out. Yes or no?
BINOMIAL DISTRIBUTION
1. Only two outcomes possible2. Fixed number of trials3. Outcomes are independent of one
another4. Probability of a success remains the
same for each trial
Binomial Distribution or not?1. You are going to toss a coin 4 times.
Determine how many times you get tails.
2. Sallies is in the bonus for a 1 and 1 situation. Michael is an 82% shooter. Michael’s outcome is noted.
3. From Del State Police: 16% of victims of car accidents were minors (under 21). A random sample of 100 accidents is selected and the number of minors killed is noted.
Binomial Dist.
NOT a Binomial Dist.
Binomial Dist.
Ask yourself the four questions.
Are there 2 outcomes?Is there a fixed number of trials?Are the outcomes independent?Does the probability remain the same for any trial?
Binomial Distribution formula
p(success) = pp(failure) = qn = total number of trialsx = selected number out of
totalx n x
n xC p q
Quiz time1. What is the most difficult self-
discipline challenge for people? 2. The human brain is 80% of this.3. Bluebirds cannot see this color.4. Flamingos do this to cool down.5. Who were the first father son pair to
be elected President of the USA?
ANSWER MAN1. What is the most difficult self-discipline
challenge for people? WEIGHT
2. The human brain is 80% of WATER
3. Bluebirds cannot see this color. BLUE
4. Flamingos do this to themselves to cool
down.? PEE on themselves
5. Father Son presidents? John Adams and
John Quincy Adams
AT MOST and AT LEAST
4) What is the probability that at most three of you passed the test?
5) What is the probability that at least nineteen of you passed the test?
Variance and Standard Deviation
The variance of a binomial distribution is:
The standard deviation of a binomial distribution is:
variance npq
. . variances d npq
DICE GAMES1) A die is rolled 600 times. Find the
mean, variance, and standard
deviation of the number of 4’s that
are rolled.
x np
n = total number = 600p = p(success) = p(4) = 1/6
mean = 600(1/6) = 100
variance npqq = p(failure) = p(not 4) = 5/6
variance = 600(1/6)(5/6) ≈ 83.333
. . variances d npq 83.3333 9.1287
VACATION!!!!2) Liberty Travel finds that 7% of all vacation
packages are canceled each year. If they estimate
500 packages a year, how many can they expect
will be canceled (aka find the mean)?
3) Find the variance and standard deviaton.n = total number = 500p = p(success) = p(cancel) = 7%q = p(failure) = p(not cancel) = 93%mean = 500(7%) = 35variance = 500(7%)(93%) = 32.55
32.55 5.705
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