Respuesta :
Answer:
Probability that exactly two people out of a randomly chosen group of five people have responded to a telephone call-in poll is 0.264.
Step-by-step explanation:
We are given that according to a recent New York Times poll, 25% of the public have responded to a telephone call-in poll.
Also, five people have people have been randomly selected.
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]
where, n = number trials (samples) taken = 5 people
r = number of success = exactly two
p = probability of success which in our question is probability that
public have responded to a telephone call-in poll, i.e; p = 25%
Let X = Number of people who have responded to a telephone call-in poll
So, X ~ Binom(n = 5, p = 0.25)
Now, probability that exactly two people out of group of five people have responded to a telephone call-in poll is given by = P(X = 2)
P(X = 2) = [tex]\binom{5}{2} \times 0.25^{2} \times (1-0.25)^{5-2}[/tex]
= [tex]10 \times 0.25^{2} \times 0.75^{3}[/tex]
= 0.264
Therefore, the probability that exactly two people out of a randomly chosen group of five people have responded to a telephone call-in poll is 0.264.
