Binomial Distribution Y12 Flashcards
What can be said about n, the number of trials, when finding a binomial probability distribution?
n must be fixed
What can be said of the number of outcomes when finding a binomial probability distribution?
There must be only two outcomes, win or lose
A win could be described as someone being over 6ft tall or hitting bullseye and a loss as someone less than 6ft or missing bullseye
What can be said of the probability of success for each trial for a binomial probability distribution?
Probability of success must be the same for each trial
All trials must be independent
What is the notation for binomial probability distribution?
X - B (n , p)
where:
- n is the number of trials carried out
- p is the probability of success
Is the following statement capable of being modelled with a binomial distribution or not?
‘You are given a fair coin and must keep tossing until you obtain 4 heads in succession’
No,
there are not a fixed number of trials so there is no value for n
Is the following statement capable of being modelled with a binomial distribution or not?
‘Given 15% of people have A+ blood, find the number of pupils in a geography class of 14 who have A+’
Yes,
n = 14
p = 0.15
So, X - B (14 , 0.15)
What does binomial probability distribution say for the probability of x?
P ( x = …….)
What does binomial cumulative distribution say for the probability of x?
P ( x is less than or equal to …….)
How do you use your calculator for binomial pd / cd?
MENU (7)
for binomial pd, (4)
for binomial cd, down 1
then (2)
enter data using =
What is the expected value of a distribution [E(X)]?
The long-term average
If the event was repeated many times, the expected value should be the average of these outcomes
What is the ‘formula’ for the expected value?
E(X) = np
