6 2 binomial probability distribution
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6.2 Binomial Probability Distribution. Objectives: By the end of this section, I will be able to… Explain what constitutes a binomial experiment. Compute probabilities using the binomial probability formula. Find probabilities using the binomial tables.

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6.2 Binomial Probability Distribution

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6 2 binomial probability distribution

6.2 Binomial Probability Distribution

Objectives:

By the end of this section, I will be

able to…

  • Explain what constitutes a binomial experiment.

  • Compute probabilities using the binomial probability formula.

  • Find probabilities using the binomial tables.

  • Calculate and interpret the mean, variance, and standard deviation of the binomial random variable.


6 2 binomial probability distribution

Life

  • There 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

BINOMIAL DISTRIBUTION

Only two outcomes possible

Fixed number of trials

Outcomes are independent of one another

Probability of a success remains the same for each trial


Binomial distribution or not

Binomial Distribution or not?

Binomial Dist.

  • You are going to toss a coin 4 times. Determine how many times you get tails.

  • Sallies is in the bonus for a 1 and 1 situation. Michael is an 82% shooter. Michael’s outcome is noted.

  • 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.

Ask yourself the four questions.

Are there 2 outcomes?

NOT a Binomial Dist.

Is there a fixed number of trials?

Are the outcomes independent?

Does the probability remain the same for any trial?

Binomial Dist.


Binomial distribution formula

Binomial Distribution formula

p(success) = p

p(failure) = q

n = total number of trials

x = selected number out of total


Quiz time

Quiz time

  • What is the most difficult self-discipline challenge for people?

  • The human brain is 80% of this.

  • Bluebirds cannot see this color.

  • Flamingos do this to cool down.

  • Who were the first father son pair to be elected President of the USA?


Answer man

ANSWER MAN

  • What is the most difficult self-discipline challenge for people? WEIGHT

  • The human brain is 80% of WATER

  • Bluebirds cannot see this color. BLUE

  • Flamingos do this to themselves to cool down.? PEE on themselves

  • Father Son presidents? John Adams and John Quincy Adams


6 2 binomial probability distribution

  • Passing Grade is 3, 4, or 5 correct.

  • How many students passed?

  • How many students failed?


Exactly

EXACTLY

1) What is the probability that exactlyseven of you passed the quiz?


At most and at least

AT MOST andAT 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?


6 2 binomial probability distribution

This is the same as saying “exactly4.”


6 2 binomial probability distribution

This is the same as saying “at most 2.”


Mean of the binomial distribution

Mean of the Binomial Distribution

μ

= mean

n = total number

p = probability of success


Variance and standard deviation

Variance and Standard Deviation

  • The variance of a binomial distribution is:

  • The standard deviation of a binomial distribution is:


Dice games

DICE GAMES

1) A die is rolled 600 times. Find the mean, variance, and standard deviation of the number of 4’s that are rolled.

n = total number = 600

p = p(success) = p(4) = 1/6

q = p(failure) = p(not 4) = 5/6

mean = 600(1/6) = 100

variance = 600(1/6)(5/6) ≈ 83.333


Vacation

VACATION!!!!

  • 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)?

  • Find the variance and standard deviaton.

n = total number = 500

p = p(success) = p(cancel) = 7%

q = p(failure) = p(not cancel) = 93%

mean = 500(7%) = 35

variance = 500(7%)(93%) = 32.55


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