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## Stat 200

1 review
by: Michael Citrenbaum

24

2

3

# Stat 200 Stat 200

Michael Citrenbaum
Penn State

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Notes for Normal Distributions and binomials
COURSE
Elementary Statistics
PROF.
Patricia Buchanan
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
Statistics
KARMA
25 ?

## 2

1 review
"These were really helpful...I'll be checking back regularly for these"
Tremayne Windler

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Michael Citrenbaum on Thursday January 28, 2016. The Class Notes belongs to Stat 200 at Pennsylvania State University taught by Patricia Buchanan in Winter 2016. Since its upload, it has received 24 views. For similar materials see Elementary Statistics in Mathematics (M) at Pennsylvania State University.

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## Reviews for Stat 200

These were really helpful...I'll be checking back regularly for these

-Tremayne Windler

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Date Created: 01/28/16
Stat 200 Probability and Distributions Random Variables: Discrete vs. Continuous Discrete:  Countable number of distinct values  Usually whole numbers  Typically used when a variable doesn’t have too many choices Continuous:  Assumes a range of values  Often need a measuring instrument  Can come from a calculation X=Number of stars TV is rated K P (x=k) 1 0.2 2 0.05 3 0.1 4 0.2 5 0.45 Total 1.00t What is the probability of having at most 2 stars? 0.20+0.05=0.25 At least 3 stars? 0.1+0.2+0.45=0.75 More than 3 stars? 0.2+0.45=0.65 Mean= 1(0.2)+2(0.05)+3(0.1)+4(0.2)+5(.45)= 3.65 star Binary Models  Have an n (meaning number or sample size).  Success/Failure Example: n= 1,009 trials ­Success= drink at least one cup of coffee a day ­Failure= none Randomization is used for choosing the 1,009 people P=0.04 (4%) N (population)=250 Million and n(sample size)=1,009 A. Number of textbooks=Discrete because textbooks are a whole number and non­binomial  because there are no failures or successes. B. For Twitter or not=binomial C. X=Student’s blood level of Vitamin D=continuous because blood is not necessarily a  whole number D. Birthday=Continuous because not everyone has birthday on same day of year. ­Non­binomial always means discrete Normal Distributions: Bell­Shape Total area under the curve is always 1. ­What is the probability that z is greater than 1? P(z>1)=.1587 P(z=1)=0 Middle half of data is always 68 percent. Therefore, 34 percent on each side meaning approximately 16 percent is 1 standard deviation  away, hence .1587 As n increases all binomials look more normal For example p=0.57 looks somewhat normal at n=10 but more normal at n=100 For example p=0.2 appears right­skewed when n=10 but a normal distribution at n=200

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