An insurance company issues 1300 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2.5. Assume the numbers of claims filed by distinct policyholders are independent of one another.
Find the approximate probability that the number of total claims during a one-year period is between 3141 and 3387.
Enter your answer as a number accurate to 4 decimal places.
Enter your answer as a number accurate to 4 decimal places.