Thread: Help with binomial distribution

In a particular city, it is believed that 30% of people who
are eligible to vote there, support the Liberal Democrat party.
If 31 people (who are eligible to vote there) are selected at random, what is
the probability that the following number will support the Liberal Democrats?
Giving your answers to 4 decimal places, use Excel to find the following:
(a) more than 10
(b) Fewer than 6
(c) exactly 9
(d) What is the expected number of people to support the Liberal Democrats?
(e) Assuming all members of the sample support a political party, how many are expected to support another party?
Can someone please go answers with me/how to do it in excel. I would be extremely grateful.

Hey Ceidon.

Google returned that the function is BINOMDIST:

Binomial Probabilities in Excel

Originally Posted by chiro

Hey Ceidon.

Google returned that the function is BINOMDIST:

Binomial Probabilities in Excel

Can you show me how to use the excel function to solve the problems, I'm really confused

The example is shown at the bottom of the link:

To find the probability in the binomial P(X = x) for n trials, p - probability of ai success, and a given x we use

=binomdist(x,n,p,false)

For a probability P(X < x) with same definitions above we use:

=binomdist(x,n,p,true)

Originally Posted by chiro

The example is shown at the bottom of the link:

To find the probability in the binomial P(X = x) for n trials, p - probability of ai success, and a given x we use

=binomdist(x,n,p,false)

For a probability P(X < x) with same definitions above we use:

=binomdist(x,n,p,true)

Would you mind aplying it to the actual questions as I'm not sure how to do it myself. Sorry if I sound retarded, I.m not too good with math and I would really appreciate your help.

I'll provide an example for the first question:

More than 10.

Cumulative = true
n=31,
x=10
p=0.3

Note: when I said P(X < x) i should have said P(X <= x) instead.

So since P(X > x) = 1 - P(X <=x) then

P(X > 10) is in excel

=(1-binomdist(10,31,0.3,true)).

Note that you may have to use algebraic expressions of the function. I have used 1 - P(X > 10) in this example (it won't always be simply =binomdist(whatever)).

Originally Posted by chiro

I'll provide an example for the first question:

More than 10.

Cumulative = true
n=31,
x=10
p=0.3

Note: when I said P(X < x) i should have said P(X <= x) instead.

So since P(X > x) = 1 - P(X <=x) then

P(X > 10) is in excel

=(1-binomdist(10,31,0.3,true)).

Note that you may have to use algebraic expressions of the function. I have used 1 - P(X > 10) in this example (it won't always be simply =binomdist(whatever)).

Thanks for that I can do the next questions now but would you mind showing me how to do questions d and e. I'm still confused about that, sorry I know it's a lot to ask

For d) do you know how to calculate the expectation of a distribution (in terms of x and P(X = x)?)

Originally Posted by chiro

For d) do you know how to calculate the expectation of a distribution (in terms of x and P(X = x)?)

no, can you show me how do it please?

Originally Posted by chiro

For d) do you know how to calculate the expectation of a distribution (in terms of x and P(X = x)?)

Please show me how to get the answers to questions d and e. It's really important that I get it right.

For d) you will need to calculate P(X=x) for all values of x using binomdist.

So in excel if you have a spreadsheet with a free column, then do the following:

=binomdist(x,31,0.3,false) for all values of x (do fill down)

in other column do a fill down for the values of x

In another column calculated the product of the two adjoining cells for each row.

Then for this last column add up all the values to get your expectation.

For your last question you have to estimate the parameter p from the sample.

The typical way to estimate given a large enough sample is to use p_hat = number_of_successes/number_of_trials and p_var = SQRT(p_hat*(1-p_hat)/number_of_trials where number_of_trials is the sample size.

Relative to this sample, if it is an unbiased sample (and that is a big assumption), then use the above to calculate a confidence interval.

Since you haven't given a sample, your question can't be answered until you do.