Binomial Distribution: beetroot seed germination

[Monkeyseat]

Answers from the following table:

9) A gardener plants beetroot seeds, the probability of a seed not germinating is 0.35, indepedently for each seed.

Find the probability that, in a row of 40 seeds, the number not germinating is:

a) nine or fewer
From the table (nine or less); 0.0644
b) seven or more,
From the table (seven or more = 1 - 6 or less); 1 - 0.0044 = 0.9956
c) equal to the number germinating.

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I am stuck on (c), I realise that it should be 20 germinating and 20 not but I don't know how to get this from the table. I know that:

= 0.0190

But how can I get the same answer from the cumulative binomial table? I just want to know how to do that as I have done all the other questions using the table. Sorry for the pictures but I don't know how to type that kind of math.

Many thanks. I've not been doing binomial distribution for long so go slowly.

Cheers.

 

[pka]

Re: Binomial Distribution (2)

Given a binominal random variable X with probability p and N trials, if we have k successes then we have N-k failures.
The probability of exactly k successes is exactly the same as N-k failures.
To see that note these facts.
\(\displaystyle {N \choose K} = {N \choose {N-k}}\)
\(\displaystyle P(X = k) = {N \choose K}p^k \left( {1 - p} \right)^{N-k} = {N \choose {N-k}}p^k \left( {1 - p} \right)^{N - k} = P\left( {X = N-k} \right)\)

 

[Monkeyseat]

Re: Binomial Distribution (2)

\(\displaystyle {N \choose K}p^k \left( {1 - p} \right)^{N-k}\)

Isn't that what I did? Here:

= 0.0190

Sorry, I was just a bit confused by your reply as I have not been doing this long. I appreciate your assistance, please could you give me a clue as to how to get the answer from the cumulative binomial table in my original post? This is what we have been doing in class and I am just wondering if it can be done this way.

Many thanks.

EDIT:

I've got the answer using the table method now.