lab3.pdf - Lab 3 The Normal Distribution INST 314 Fall 2018 Let’s start as always by bringing in the packages that we’ll be using require(openintro

# lab3.pdf - Lab 3 The Normal Distribution INST 314 Fall 2018...

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Lab 3: The Normal Distribution INST 314 Fall 2018 Let’s start as always by bringing in the packages that we’ll be using. require (openintro) require (dplyr) require (ggplot2) Using pnorm() and associated functions There are a suite of functions for using the Normal distribution. You can look at these by looking at the help file for any of them. ?pnorm Using pnorm() The pnorm() function finds the proportion that is below a certain value on the Normal distribution. This, as with the other Normal distribution functions, have a default value of 0 for the mean and 1 for the standard deviation. pnorm ( 2 ) # Proportion below 2 in a N(0,1) ## [1] 0.9772499 pnorm ( 2 , mean = 1 , sd = 0.5 ) # Proportion below 2 in N(1,0.5) ## [1] 0.9772499 Recall that finding a z-score basically puts all values in a Normal distribution on the same Standard Normal distribution, with a mean of 0 and a standard deviation of 1. Regardless of the scale, though, the same proportion of values will be below. For example, consider an exam that had scores distributed Normal with a mean of 60 and a standard deviation of 6. If a person scored a 68 on that exam, then their z-score would be (68 - 60) / 6 = 1 . 33 . We can then find the proportion of students they did better than.

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