Modelling with the Binomial Distribution

Question 1

How do you write binomial distribution?

Answer 1

X ~ B(n, p)

Question 2

How do you work out the mean (μ)?
(binomial distribution)

Answer 2

n x p

Question 3

How do you work out the variance (σ^2) ? (binomial distribution)

Answer 3

np(1-p)

Question 4

What modelling assumptions do you need to meet for binomial assumptions?

Answer 4

there is a fixed number of trials (n)
there are two possible outcomes (‘success’ or ‘failure’)
there is a constant probability of success
the trials are independent

Question 5

What does it mean if the means are similar?

Answer 5

the probability is probably correct

Question 6

What does it mean if the variances differ?

Answer 6

we could have a problem with the sample not being random or outcomes not being independent

Question 7

How would you answer this question? :

sample size n= 40 from population {x} gives x̄=6.14 s^2=2.39
Discuss whether X~B(20,0.3) is an appropriate model.

Answer 7

work out the mean of the binomial distribution by working out np, and the variance by working out np(1-p)
in this Q mean of BD=np=20(0.3)=6
compare this to sample mean which is 6
so means are similar
variance of BD=np(1-p)=20 x 0.3(1-0.3) = 4.2
sample variance=2.39
variances are not similar
therefore the binomial model is not appropriate