Understanding Poisson to Normal Approximation

[big man]

Homework Statement

I'm trying to understand the poisson to normal approximation. I've got this book that says the poisson distribution approximates the normal distribution well when the mean is greater than 100.


2. understanding/interpretation
Let's call N the number of counts observed when observing a star for example.
Let's also say that I observe this star 300 times getting N counts over t seconds each time.

So if we apply the above "poisson to normal approximation" statement to the situation I just outlined then is this right:

If the mean number of counts observed from the 300 trials is greater than 100, then the poisson distribution will approximate a normal distribution pretty well.

Is this correct? I would really appreciate any confirmation/rejection of this because I'm studying for my exam for tomorrow and this is a small thing I'm not too sure about.

Thanks in advance

 

[mighty2000]

I can confirm that the statement about the Poisson distribution approximating the normal distribution well when the mean is greater than 100 is correct. In your example, if the mean number of counts observed from the 300 trials is greater than 100, then the Poisson distribution can be used as an approximation for the normal distribution. However, it is important to note that this is not a perfect approximation and there may be some discrepancies between the two distributions. This approximation is often used in cases where the sample size is large and the mean is relatively large, as it simplifies calculations and makes them more manageable. I hope this helps and good luck on your exam!