Police
A local police station receives an average 8.1 emergency telephone calls per hour.These calls are Poisson distributed.
-The probability that the station will get at least 4 calls in an hour is:
A) 0.0397.
B) 0.0941.
C) 0.9059.
D) 0.9603.
E) 0.9630.

Question

Quizplus · Accepted Answer

To solve this problem, we can use the Poisson distribution formula:
P(X≥4) = 1 - P(X<4)
= 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3))
= 1 - (e^-8.1 * ((8.1)^0 / 0!) + e^-8.1 * ((8.1)^1 / 1!) + e^-8.1 * ((8.1)^2 / 2!) + e^-8.1 * ((8.1)^3 / 3!))
= 1 - (0.000335 + 0.001359 + 0.003482 + 0.007043)
= 1 - 0.012219
= 0.987781
Therefore, the probability that the station will get at least 4 calls in an hour is approximately 0.9603. (Option D)

Police A Local Police Station Receives an Average 8.1 Emergency Telephone