What is the Proportion of Weeks with High or Low Deaths in the 1980s?

[knowLittle]

In the 1980s, an average of 121.95 workers died on the job each week. Give estimates of the following quantities:
a.) the proportion of weeks having 130 deaths or more;
b.) the proportion of weeks having 100 deaths or less.
Explain your reasoning.

Procedure
I'm not sure, how to start. This might not be a Poisson or Binomial R.V.

Could someone help?

 

[moonman239]

Ideally you need to know more about the distribution of the number of deaths each week.

 

[sid9221]

What you could do is write down the formula for a Confidence Interval with the upper interval 130 and lower 100, with mean 121.95 and work out the "percentage value". Divided by 2 that would give you what you need.(I think)

Now you would need to know the distribution to do this, So if you think it may be the Poisson or Binomial try it, but intuitively I don't see how those distributions would fit this type of data.

I would try the Normal Distribution

 

[chiro]

In the 1980s, an average of 121.95 workers died on the job each week. Give estimates of the following quantities:
a.) the proportion of weeks having 130 deaths or more;
b.) the proportion of weeks having 100 deaths or less.
Explain your reasoning.

Procedure
I'm not sure, how to start. This might not be a Poisson or Binomial R.V.

Could someone help?

Hey knowLittle.

The first thing you need to ask for this rate process is if every death realized is independent of every other death realized for this rate process for the entire period of all data collected.

In practice you can't really use this assumption because in a case like this, instances of deaths will for example change or introduce legislation to make work-places safer and things like this.

Because of this modelling deaths in workplace accidents is not an independent process reflecting a true Poisson process, but something different.

In terms of what a Poisson distribution is, it's just a limiting case of the binomial distribution where an interval shrinks to zero as the result of a limit.

If you want to use a Poisson distribution (and I think your question is implying this) then estimate the parameters (i.e. the value of λ) and use the CDF of the distribution to obtain an answer.

But again for practicality, I stress that you need to understand what independence means and when it is a safe assumption to use and when it is not a safe assumption to use because in a case like this, if you modeled death rate processes using an independent assumption, especially over a long time period that had many amendments and introduction of legislation and safety laws, then you're analysis will be useless and your recommendations will be useless.

 

[oleador]

I think we can apply the Central Limit Theorem here (correct me if I'm wrong). The number of observations should be large enough to use the CLT -- the death rate was measured weekly for several years. Then by the CLT the distribution of weekly death rates should converge to the normal distribution. Note, that we need to assume that each death occurs independently. This will not be strictly true, but the assumption is not very strong.

To be more precise, the CLT says that: given a sequence of random variables $X_n$ (in our case each $X_n$ is the number of deaths in week $n$), as $n→∞$ $(\sum X_n)/n$ converges to the normal distribution with mean 121.95 and ? variance. Is there any information on variance?