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Q: What are the requirements for a probability distribution (Select all that apply.)?
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Does empirical rules always apply to discrete probability distribution?

the empirical rules of probablility applies to the continuous probability distribution


How does the probability theory apply to statistics?

Statistics is the study of how probable an observed event is under a set of assumptions about the underlying probability distribution.


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Assuming that the requirements of normality are met, a statement such as the parameter M has the value m, with a 95% confidence interval of (m-a, m+b) means that there is a 95% probability that the true value of M lies between m-a and m+b.


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Why the normal distribution can be used as an approximation to the binomial distribution?

The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.


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Yes, If you have a large data set, you can approximate the discrete data by Normal distribution (which is continuous). An example would be, "A coin is tossed 1000 times. What is the probability of rolling between 300 and 400 heads?" This problem, usually solved by Binomial distribution (which is a discrete distribution), is very difficult to solve because of the large data set and can be approximated by the Normal distribution.


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