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)0.1494
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 (or half a minute). Using the Poisson probability formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (3 in this case) and k is the number of errors (1), we calculate the probability of 1 error in 30 seconds. This results in approximately 0.1494.

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