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When an opinion poll calls residential telephone numbers at random, only 20% of the phone calls...

When an opinion poll calls residential telephone numbers at random, only 20% of the phone calls reach a live person. X is the number of calls that reach a live person out of 20 dialings from the random digit dialing machine.

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Answer #1

When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random digit dialing machine make 20 calls.

a) What is the probability that exactly 4 calls reach a person?
b) What is the probability that at most 4calls reach a person?
c) What is the mean number of calls that reach a person?
d) What is the standard deviation of the count of calls that reach a person?

Answer :

Here the distribution is binomial one

where n = 20 and p = 0.20

(a) If x is the number of right calls

Pr(x = 4) = 20C4 (0.20)4 (0.80)16 = 0.2182

(b) Pr(X <= 4) = 0.6296

(c) Mean number of calls = 20 * 0.20 = 4

(d) standard deviation = sqrt(20 * 0.20 * 0.80) = 1.7889

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