SOLUTION: The average number of phone calls/minute coming into a switch board between 2 p.m. and 4 p.m. is 2.5. Determine the probability that during one particular minute there will be i.

Algebra ->  Probability-and-statistics -> SOLUTION: The average number of phone calls/minute coming into a switch board between 2 p.m. and 4 p.m. is 2.5. Determine the probability that during one particular minute there will be i.       Log On


   

Question 976034: The average number of phone calls/minute coming into a switch board between 2 p.m. and 4 p.m. is 2.5. Determine the probability that during one particular minute there will be
i. 4 or fewer
ii. more than 6 calls
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We use the Poisson probability distribution to solve
Probability(P)(X for given lamda) = e^(-lamda)*lamda^X / X!
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lamda for the problem is 2.5
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i) P( X < or = 4 ) = P(0) + P(1) + P(2) + P(3) + P(4)
P(0:2.5) = 0.082084999
P(1:2.5) = 0.205212497
P(2:2.5) = 0.256515621
P(3:2.5) = 0.213763017
P(4:2.5) = 0.133601886
P( X < or = 4 ) = 0.89117802 approx 0.89 or 89%
ii) P ( X > 6 ) = 1 - P( X < or = 6 )
P(5:2.5) = 0.066800943
P(6:2.5) = 0.027833726
P ( X > 6 ) = 1 - 0.985812689 approx 0.01 or 1%