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Probability The average time between incoming calls at a switchboard is 3 minutes.if a call has just come in,the probability that the next call come within the next t minutes.is p(t) = 1 -e - t/3 Find the probability of each situation.
(a) A call in comes within 1/2 minutes.
(b) A call in comes within 2 minutes.
(c) A call in comes within 5 minutes.

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Answer:

a) 0.1535

b) 0.4866

c) 0.8111

Step-by-step explanation:

The probability that the next call come within the next t minutes is:

  • [tex]p(t) = 1 -e ^{- t/3}[/tex]

According to this model,

a) the probability that a call in comes within 1/2 minutes is [tex]p(t) = 1 -e ^{- (1/2)/3}[/tex] =0.1535

b) the probability that a call in comes within 2 minutes is  [tex]p(t) = 1 -e ^{-2/3}[/tex] =0.4866

c) the probability that a call in comes within 5 minutes is  [tex]p(t) = 1 -e ^{-5/3}[/tex] =0.8111

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