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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;
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%
<em><u>Let X = Number of people who have responded to a telephone call-in poll</u></em>
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) =
=
= <u>0.264</u>
<em>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.</em>