Final answer:
To find the probability of exactly 5 requests in a 2-second time interval, use the exponential distribution formula.
Step-by-step explanation:
To find the probability that there will be exactly 5 requests in a 2-second time interval, we need to use the exponential distribution formula. Let's assume that the average rate of requests is R requests per second. The formula for the exponential distribution is P(X = k) = e^(-Rt)*(Rt)^k/k!, where X is the number of requests in a given time interval, R is the average rate, t is the time interval, and k is the number of requests.
In this case, the average rate is 5 requests per minute, so R = 5/60 = 1/12 requests per second. The time interval is 2 seconds, so t = 2 seconds. Plugging these values into the formula, we get P(X = 5) = e^(-1/12*2)*(1/12*2)^5/5!.
Calculating this expression will give us the probability that there will be exactly 5 requests in a 2-second time interval.