# 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?

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