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1. Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data. Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation. When forming your answer to this question you may give an example of a situation from you own field of interest for which a random variable can serve as a model. (2-3 well composed paragraphs) 2. Describe in your own words the meaning of the number that the following R command produces (you are asked to interpret the resulting number so that we understand what that number means). pexp(1.2, rate=3) (1 paragraph) 3. Vocabulary and R functions (be sure to include an APA citation) a) What is a normal distribution? _________________ b) What does the pnorm() function do?_________________________ 4. If you know the mean and standard deviation of a normally distributed population, and somebody asks you questions about the highest 1% and lowest 1% of numbers in that population, what could you tell them? Pick your own values for the mean and standard deviation and then answer the question for those values. Choose one of these R functions to answer the question: dnorm(), pnorm(), qnorm(), rnorm(). (2-3 well composed paragraphs)