Probabilities and Binomial Distributions

Suppose $X$ is a binomial random variable with $n = 25$ and $p = 0.7$. Use Excel or Minitab to find the following. Please give the answers to five decimal places.

$$P(X = 16) = ?$$

I used the excel binomial distribution function and it is saying my answer is wrong. I put $0.67693$, and was wondering if it is correct?

2 Answers

If the question is asking for greater than or equal to $16$, the answer would be

$1-P(X<=15)=1-binocdf(15,25,0.7)=0.810563976495052$

where I have used GNU Octave's binomial CDF function called $binocdf()$.

• This was correct, thank you! – Jake Nagel Mar 16 '14 at 17:53
• Why is it the compliment of less than fifteen? – Jake Nagel Mar 16 '14 at 17:53
• It is the complement of less than or equal to $15$, as you want the probability of $X$ being $16$ or more. – Alijah Ahmed Mar 16 '14 at 18:32

We should calculate $C_{25}^{16}0.7^{16} 0.3^9$, right?

wolfram gives http://www.wolframalpha.com/input/?i=Binomial%5B25%2C16%5D%280.7%5E16%29%280.3%5E9%29

the answer is 0.1336358513921865558356925

• Thanks for the input. I tried several different things including this answer but the online homework is saying this is incorrect. Im starting to wonder if its an error with the program? The question is asking for greater than or equal to 16 – Jake Nagel Mar 16 '14 at 9:50
• If I am the quesion designer, I may check the use of poission distribution to approximate binomial distribution. This is just my guess. – Frazer Mar 16 '14 at 10:10
• Jake: In your problem statement you asked for the probability that X=16. In the comment above you say the question is asking for the probability that X >= 16. Which is it? This is probably the cause of your confusion. – awkward Mar 16 '14 at 13:53
• The question asks for greater than or equal to 16. I think it might have been corrected by the site after I posted it. – Jake Nagel Mar 16 '14 at 17:48