Find the mean & St. Dev for each.

  Mean St. Dev

X 8 3

Y 12 4

4 7x 3 2x y

Find the mean & standard deviation

x p(x)

4 0.2

7 0.31

12 0.24

15 0.18

18 0.07

BINOMIAL DISTRIBUTION FORMULASection 6.3A

Binomial Experiment - BINS• Binary?

• There are two possible outcomes – success and failure

• Independent?• Trials must be independent

• Number?• The number of trials must be fixed – out of n….

• Success?• On each trial the probability of success must be the same

Let E be the event that a person goes out shopping on Black Friday. Find the probability distribution for a sample of 3 people if the P(E) = .78.

Probability distribution of going shopping on black Friday for 4 people. P(E) = .78

Let’s Develop the formula!

• If I have 5 people, how many ways can I arrange them?

• How many ways can I choose 2 of the 5 who went shopping on black Friday?

• But every set of two is the same (SSNNN = SSNNN)…

Binomial Distribution

!

( )! !n x

n nC

x n x x

( ) x n xnp x p q

x

1q p where

The survival rate for a risky operation is 80%. What is the probability that exactly 4 of the next 5 patients survive?

USA today stated that 45% of Americans know somebody who became addicted to a drug other than alcohol. If we randomly ask 15 people, what’s the probability that exactly 3 were addicted?

What’s the probability that at least 12 are addicted?

What the probability that less than 3 are addicted?

90% of the trees planted by a landscaper will survive. If 10 trees are planted, what’s the probability more than eight survive?

The probability that a person will subscribe to Statistics Monthly is 48%. Find the probability that out of a group of seven, at least one person subscribes.

There are charts as well – but only for some probabilities so you need to know the formula.

Homework• Worksheet