# Binomial Probability

• Sep 21st 2011, 04:13 PM
koudai8
Binomial Probability
Hi, the following is a list of binomial cumulative distribution of the probability that out of 25 investors, the number of investors that would have exchange-traded funds in their portfolios.

We were asked for the probability that at least 14 investors do not have exchange-traded funds in their portfolios from this table.

Binomial
n 25
p 0.4800

xi P(X<=xi)
0 0.0000
1 0.0000
2 0.0000
3 0.0002
4 0.0009
5 0.0037
6 0.0124
7 0.0342
8 0.0795
9 0.1585
10 0.2751
11 0.4220
12 0.5801
13 0.7260
14 0.8415
15 0.9197
16 0.9648
17 0.9868
18 0.9959
19 0.9989
20 0.9998
21 1.0000
22 1.0000
23 1.0000
24 1.0000
25 1.0000

Here is what I did: since they ask for at least 14 do not, it means 11 or less do. So the answer is .422---the cumulative of 11 and less that do.

But when I used the Binomial Cumulative Distribution function on my calculator Binomcdf (25, 0.52, 14), I get 0.725.

Where did I do wrong?

Thanks.
• Sep 22nd 2011, 09:26 AM
steinmath
Re: Binomial Probability
Just to clarify:

p = .48 is the probability that an investor has exchange-traded funds in their portfolio.

Thus

p =.52 is the probability that an investor does not have exchange-traded funds in their portfolio.

Thus, if you want to find the probability that at most 11 people have exchange funds in their portfolio, you would use:

binomcdf(25, 0.48, 11).

The parameters are (trials, prob of success, max # of successes)

Your answer would have worked if the last parameter meant "at least k successes". But it means -at most- k successes.