Final answer:
To find the probability of 5 or more phone calls in 9 minutes, we use the Poisson distribution, knowing the average rate of calls. Calculations or statistical software are required to get the actual probability, which is not provided in the given options.
Step-by-step explanation:
To calculate the probability of 5 or more calls arriving in a 9-minute period, when calls enter a college switchboard on average of two every three minutes, we can use the Poisson distribution. The Poisson distribution is used to predict the number of events happening over a fixed period of time if these events happen with a known average rate and independently of the time since the last event.
The average rate (\(\lambda\)) for a 9-minute period is calculated by multiplying the average number of calls per three minutes (which is 2) by the number of three-minute intervals in nine minutes (which is 3): \(\lambda = 2 \times 3 = 6\). Now, using the Poisson probability formula:
\(P(X=k) = \frac{e^{-\lambda}*\lambda^k}{k!}\)
we can calculate the cumulative probability for 0, 1, 2, 3, and 4 calls and subtract it from 1 to find the probability of getting 5 or more calls, or we can use statistical software or a Poisson distribution table for this computation. The correct answer uses the complement rule where:
\(P(X \geq 5) = 1 - P(X < 5)\)
Therefore, the correct answer is not provided as an option in the given question, as further calculations or software would be needed to compute the exact probability value.