Question

According to Nielson Media Research, 65% of all United States households have cable television.
In a random sample of 20 households, which is the probability that exactly 15 have cable?

a) 0.063
b) 0.873
c) 0.127

I'm pretty sure the correct answer is c, but I'm not sure how to do the calculations.

Answer 1

You use the binomial probability distribution function
See http://en.wikipedia.org/wiki/Binomial_distribution#Probability_mass_function

Here the probability of success is 0.65

Answer 2

The probability of getting exactly k success in n trials is
\[ \Pr(k; n)= \left(\begin{matrix}n \\ k\end{matrix}\right)r^k (1-r)^{n-k}\]

Answer 3

so...
n = 20
k = 15
r = 0.65

??

Answer 4

yes

Answer 5

alright, i'll work that out and see what i get

Answer 6

You can type
(20 choose 15)*0.65^15*(1-0.65)^5=
in the google search window to get the value.

Answer 7

nice, thanks