SOLUTION: A business has several telephone lines. Incoming calls have a Poisson distribution. They come in at the rate of 1 every 75 minutes during daytime hours. What is the probability, ov

Algebra ->  Probability-and-statistics -> SOLUTION: A business has several telephone lines. Incoming calls have a Poisson distribution. They come in at the rate of 1 every 75 minutes during daytime hours. What is the probability, ov      Log On


   



Question 473883: A business has several telephone lines. Incoming calls have a Poisson distribution. They come in at the rate of 1 every 75 minutes during daytime hours. What is the probability, over the course of four daytime hours that the business receives:
(a) no calls
(b) exactly four calls
(c) exactly three calls: Show the Poisson formula and the substitution
__________________________________________________________________________
(d) at most five calls
(e) at least three calls
(f) between 3 and 7 calls, inclusive

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will answer only the first three. I know you'll get the idea for the remaining ones...
mu+=+%281%2F75%29%2A60+=+60%2F75+=+0.8
(a) P%280%29+=+e%5E%28-0.8%29%2A%280.8%5E0%2F0%21%29+=+0.4493
(b) P%284%29+=+e%5E%28-0.8%29%2A%280.8%5E4%2F4%21%29+=+0.00767
(c) P%283%29+=+e%5E%28-0.8%29%2A%280.8%5E3%2F3%21%29+=+0.038343