An event occurs with a mean of 15 times per hour and a standard deviation of 10 times/h. From the population a sample of 100 individuals is drawn. What is the probability that the sample mean will be between 14 and 16?
I want to solve this problem assuming that the event follows a Poisson distribution (I can get the right answer when assuming a normal distribution).
My R input is:
> 1-ppois(16, lambda=15, lower.tail=FALSE)-ppois(14, lambda=15)  0.1984695
ppois call gives the right tail area and the second call the lower tail area, which I both subtract from 1.
What is wrong with my calculation?