# 2/17/2023

# 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)!]*p
^{k}*(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.

## Please read Sections 4.4 and 4.5 for class on Monday.