How to Identify the right probability model?

Example 1

An airline claims that at most 6% of all lost luggage is never found. A random

sample of size 200 is taken. Out of the 200 observations (supposed to be independent) 23 pieces

of luggage were never found. Test whether the airlines claim is true at a 1% level using the

critical value method.

Example 2

The life span of a cartridge used in photocopying is measured by the number of

copies produced by the cartridge. You wish to determine whether the mean number of copies per

cartridge is greater than 17600. A random sample of n = 15 cartridges operating independently

of one another is taken and the sample average is 18212 copies. The distribution for the number

of copies produced by each cartridge is a normal variable and, from past experience, you already

know the standard deviation is 2,700 copies. Test the hypothesis that the true mean is greater

than 17600 at a 5% level of signicance using the P-value method.

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My question is what probability model needs to be used, and how do i tell? The characteristics?

Re: How to Identify the right probability model?

Hey Brennox.

You basically need to look at the various models and see what situation matches the assumptions. For a coin toss or two-outcome set of independent trials, we use binomial. For things that model rates we use Poisson. Without replacement uses other distributions like hyper-geometric.

You have to use a certain amount of judgement to know what probability model to use and you may have to derive it yourself if a common solution does not exist.

Hint: For the first one, you should look into a Binomial because the chance of losing luggage is assumed the same for each piece of luggage and all items are independent of each other.