# Return to calculations for normal distributions - see !Class-csv-Rscripts\NormalDistributionCalcs.R

## Assessing Normality

• Should we use the normal model for a given data set?
• 68-95-99.7 Rule
• Normal Quantile Plots - qqnorm in R
• Other Visual Displays

## Class Activity on using qqplots to assess Normality

• Open the R script QQPlot.R to conduct simulations that will help you develop your understand of these new plots.
• The script simulates data from normal distributions, uniform distributions, and t distributions. Look at the histograms and qqplots carefully. You can run the commands multiple times to help you distinguish general trends from chance variation.
• Describe each of the plots. Can you explain how the differences in the distributions are appearing on the normal probability plots?
• Use appropriate methods for assessing normality to see if the normal distribution would be an appropriate model for the quantitative variables from our Data Survey on Day 1.

## Binomial Experiments (A generalization of the discrete RV lab problem on the number of patients who experience side effects)

• Each random trial can result in one of only two possible outcomes.  This is called a Bernoulli trial.
• We collect data from Bernoulli trials satisfying the following:
• there are n trials;
• the n trials are independent; and
• the probability of “success” remains constant from trial to trial.
• Binomial Distribution - If X is the number of successes in n independent Bernoulli trials, then P(X=k)=n!/[k!*(n-k)!]*pk*(1-p)n-k, for k=0, 1, ..., n.
• Using RStudio for Binomial Probability Calculations
• dbinom() or pbinom() or qbinom()

## The mean (expected value) and standard deviation of a binomial random variable

• Mean (or Expected Value) of X is n*p
• Variance of X is n*p*(1-p)
• The standard deviation of X is the square root of the variance.

## Binomial Random Variables - See handout

• We will have a problem session on Monday, if you want to see some of these problems worked out by your peers.