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Probability

Question
CBSEENMA12036200

At a telephone enquiry system, the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is

  • 6/5

  • 5/6

  • 6/55

  • 6/e5

Solution

D.

6/e5

straight P space left parenthesis straight X space equals straight r right parenthesis space equals space fraction numerator straight e to the power of negative straight m end exponent space straight m to the power of straight r over denominator straight r space factorial end fraction
straight P left parenthesis straight X less or equal than 1 right parenthesis space equals space straight P left parenthesis straight X space equals space 0 right parenthesis space plus space straight P space left parenthesis space straight X thin space equals 1 right parenthesis
space equals space straight e to the power of negative 5 end exponent space plus space 5 space straight x space straight e to the power of negative 5 end exponent space equals space 6 over straight e to the power of 5

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