1. ## Poisson distribution sum

The question:
Seismic earth tremors occur at an active part of the earth's crust at the average rate of one every two days. What is most likely number of tremors to occur in a week.
What i want to know is the basis upon which the answer was reached?
How do I round of 3.5 in this situations? Normally it rounds to 4, sadly

The question:
Seismic earth tremors occur at an active part of the earth's crust at the average rate of one every two days. What is most likely number of tremors to occur in a week.
The number of tremors to occur in a week can be approximately considered to be a Poisson random variable (that's in the title of the thread!) with mean $\lambda=3.5$ (using your computation). In other words, the probability of $k$ tremors in a week is about $$e^{-\lambda}\frac{\lambda^k}{k!}$$. Compute that value for $k=0,1,2,3,\ldots$ and conclude.
The number of tremors to occur in a week can be approximately considered to be a Poisson random variable (that's in the title of the thread!) with mean $\lambda=3.5$ (using your computation). In other words, the probability of $k$ tremors in a week is about $e^{-\lambda}\frac{\lambda^k}{k!}$. Compute that value for $k=0,1,2,3,\ldots$ and conclude.