Final answer:
The probability can be calculated using a TI-83+ or TI-84 calculator and the Poisson probability distribution. Since on average the center would receive 2 emails in 6 minutes, we use poissonpdf(2,X) to find the individual probabilities. The sum of probabilities for receiving more than four emails can be obtained from these calculations.
Step-by-step explanation:
To calculate the probability that a customer service center receives more than four emails in the next six minutes, we first need to find the average number of emails received in six minutes. Since the customer service center receives about 10 emails every half-hour (which is 30 minutes), we would expect the center to receive on average 1 email every 3 minutes (10 emails / 30 minutes = 1 email per 3 minutes). Therefore, in six minutes, the service center would receive on average 2 emails (6 minutes / 3 minutes/email).
Since we are looking for the probability of receiving more than four emails in six minutes, we will be dealing with a Poisson probability distribution because we're looking at the number of events (emails received) that occur in a fixed interval of time.
Using a TI-83+ or TI-84 calculator, we can calculate this probability using the following steps:
- Press the STAT button and then press ENTER to go to the EDIT menu.
- Enter 1, 2, 3, etc., into L1, which represents the number of emails.
- Enter the corresponding Poisson probability formula into L2 which in this case would be poissonpdf(2,X), where X represents different email counts.
- Look for the probability associated with receiving more than four emails.
This involves using the cumulative probability distribution function and then subtracting from 1 to find the probability of getting more than four emails. However, please note that the actual detailed steps may vary slightly depending on the model of the calculator.