Standardizing Normally Distributed Random Variables скачать в хорошем качестве

Standardizing Normally Distributed Random Variables

I discuss standardizing normally distributed random variables (turning variables with a normal distribution into something that has a standard normal distribution). I work through an example of a probability calculation, and an example of finding a percentile of the distribution. It is assumed that you can find values from the standard normal distribution, using either a table or a computer. The mean and variance of adult female heights in the US is estimated from data found in a National Health Statistics Report: McDowell MA, Fryar CD, Ogden CL, Flegal KM. Anthropometric reference data for children and adults: United States, 2003-2006. National health statistics re- ports; no 10. Hyattsville, MD: National Center for Health Statistics. 2008. For those using R, here is the R code for the examples used in this video: American female heights example (approximately normally distributed with a mean of 162.2 and a standard deviation of 6.8). Finding the probability that a randomly selected female is taller than 170.5 cm. Easiest way: 1-pnorm(170.5,162.2,6.8) [1] 0.111121 Standardizing route: 1-pnorm((170.5-162.2)/6.8,0,1) [1] 0.111121 The default in R's pnorm is the standard normal distribution (mean=0, SD=1), so the mean and SD can be left out when dealing with the standard normal. 1-pnorm((170.5-162.2)/6.8) [1] 0.111121 Finding the probability that a randomly selected female has a height between 150.5 and 170.5. Easiest way: pnorm(170.5,162.2,6.8)-pnorm(150.5,162.2,6.8) [1] 0.8462162 Standardizing route: pnorm((170.5-162.2)/6.8)-pnorm((150.5-162.2)/6.8) [1] 0.8462162 10th percentile of heights of adult American females. Easiest: qnorm(.1,162.2,6.8) [1] 153.4854 Alternatively, via the standard normal distribution: qnorm(.1) [1] -1.281552 That's the 10th percentile of the standard normal distribution. Converting to the distribution of heights, -1.281552*6.8+162.2 [1] 153.4854