Find the mean & St. Dev for each.
Mean St. DevX 8 3Y 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 nCx 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