In a certain communications system,there is an average of 1 transmission error per 10 seconds.Assume that the distribution of transmission errors is Poisson.The probability of 1 error in a period of one-half minute is approximately ________
A) 0.1493
B) 0.3333
C) 0.3678
D) 0.1336
E) 0.03

Question

Quizplus · Accepted Answer

The average rate of errors is 1 error per 10 seconds, which translates to 3 errors per 30 seconds (half a minute). Using the Poisson probability formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (3), k is the number of errors (1), we find P(X=1) ≈ 0.1493.

In a Certain Communications System,there Is an Average of 1