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A representative of a market research firm contacts consumers by phone in order to conduct surveys. The specific consumer contacted by each phone call is randomly determined. The probability that a phone call produces a completed survey is 0.25. Calculate the probability that more than three phone calls are required to produce one completed survey.

Respuesta :

JeanaShupp

Answer: 0.421875

Step-by-step explanation:

According to the geometric distribution,

The probability that x number of trials take place until the first success occurs will be

[tex]P(X=x)=(q)^{x-1}p[/tex], where p is the probability of getting success in each trial.

Given : The probability that a phone call produces a completed survey is p=0.25.

then q=1-0.25=0.75

Now, the probability that more than three phone calls are required to produce one completed survey :

[tex]P(X>3)=1-P(X\leq3)\\\\=1-(P(1)+P(2)+P(3))\\\\=1-((0.75)^{1-1}(2.5)+(0.75)^{2-1}(2.5)+(0.75)^{3-1}(2.5))=0.421875[/tex]

Hence, the probability that more than three phone calls are required to produce one completed survey = 0.421875

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