This is probably an unnecessary question, but how would I know given a problem when it's appropriate to use a chi-square test vs. binomial or normal distribution in a problem? Let's say that the example is dice and which numbers it lands on.
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The chi-square test is used to test how well a certain number of outcomes are following a given distribution.
The binomial and normal distributions are two specific distributions. Once you decide that your problem is modelled by one of them you can use them to calculate theorical statistics such as average or percentile values.
If you need to model the outcomes of a die, then you would use a discrete uniform distribution, where all the outcomes are equally probable and with probability of 1/6.