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Poisson vs. Gaussian distribution

Radiation: The atoms of a radioactive element are randomly disintegrating and
emitting alpha particles. The number of alpha particles emitted per second from
these atoms during a 30 second period is recorded as follows.
9.38
8.08
8.36
10.44
9.44
8.05
17.78
7.56
14.17
6.73
9.81
4.79
11.98
9.48
6.32
14.23
13.02
5.99
7.05
11.62
10.81
7.94
9.47
12.05
7.78
12.95
6.87
16.65
10.73
10.33

Trying to find best mathematical distribution model that fits the process

1 Assume that this alpha particle emission process follows a Poisson distribution. Find the parameters of this Poisson distribution. For a
Poisson distribution <x>=lambda and variance=square root of lambda)

Is this a good approximation?

2 Find a Gaussian distribution that approximates the number of alpha
particles emitted from these atoms per second.

3 Which distribution approximates the data more accurately? What is your measure of accuracy?

4 What is the probability of having more than 12 alpha particles emitted from these atoms per second? (Have you decided which distribution best describes the data?)

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