Probability of at Least 14 Not Having ETFs in 25 Investor Portfolios

[koudai8]

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.

 

[chiro]

Hey koudai8 and welcome to the forums.

Since we are given P(X = x) = probability that x people have exchange traded funds, then what is the probability P(Y = y) where y people do not have exchange traded funds related to P(X = x) (In other words how can we write P(Y = y) in terms P(X = x)?

 

[koudai8]

Is it not 0.52? (probability)

 

[M-quest]

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..

Atleast 14 do not means 13 or less do,not 11 or less.The compliment of atleast 14 is atmost 13.