# Binomial Conditions - Miami-Dade County Public Schools

Binomial v. Geometric The primary difference between a binomial random variable and a geometric random variable is what you are counting. A binomial random variable counts the number of "successes" in n trials. A geometric random variable counts the number of trials up to and including the first "success." Binomial vs. Geometric

The Binomial Setting The Geometric Setting 1. Each observation falls into 1. one of two categories. 2. The probability of success 2. is the same for each observation. 3. The observations are all independent. Each observation falls into

one of two categories. The probability of success is the same for each observation. 3. The observations are all independent. 4. There is a fixed number n of observations. 4. The variable of interest is

the number of trials required to obtain the 1st success. FRQ Answers Must Include: 1. Name of distribution Geometric, Binomial 2. Parameters Binomial: X (define variable), n & p Geometric: X (define variable), p 3. Probability Statement

Ex: P (X = 7) or P (X 3) 4. Calculation and p-value Calculator notation is okay, but needs to be labeled. 5. Solution interpreted in context. Calculator: PDF PDF = precisely (exactly) a certain value Example: P (X = 2) TI 84: binompdf(n,p,r) TI 89: binomial Pdf

n = number of trials p = probability of success r = number of success Calculator: CDF CDF = cumulative distribution. The probability of getting that value or something smaller. Example: P (X 3) TI 84: binomcdf(n,p,r) TI 89: binomial Cdf n = number of trials

p = probability of success r = number of success Calculator: 1- CDF 1 cdf = The probability of getting that value or something greater Example: P (X 8). 1 bimoncfd (n-1, p, r) *** Must reduce n by 1, too*** Twenty-five percent of the customers entering a grocery

store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use the express checkout. What is the probability that two customers used the express check out? Twenty-five percent of the customers entering a grocery store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use the express checkout. hat is the probability that two customers used the express check out?

Binomial Distribution N= 5 P = 0.25 X = # of people use express P (X =2) Twenty-five percent of the customers entering a grocery store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use

the express checkout. What is the probability that two customers used the express check out? binompdf(5, 0.25, 2) = .2637 5= number of customers 0.25= probability of success 2= number of successes desired There is a 26.37% chance that exactly 2 customers will use the express checkout lane between 5pm and 7pm. Binomial & Normal

The binomial distribution can be approximated well by a normal distribution if the number of trials is sufficiently large. A normal distribution can be used to approximate the binomial distribution if np is at least 10 and n(1-p) is at least 10. Suppose we have data that suggest that 3% of a companys hard disc drives are defective. You have been asked to determine the probability that the first defective hard drive is the fifth unit tested.

Suppose we have data that suggest that 3% of a companys hard disc drives are defective. You have been asked to determine the probability that the first defective hard drive is the fifth unit tested. Geometric Distribution P = 0.03 X = # of disc drives till defective P (X = 5) Suppose we have data that suggest that 3% of a

companys hard disc drives are defective. You have been asked to determine the probability that the first defective hard drive is the fifth unit tested. Geometpdf (0.03, 5) 0.03= p = probability of defect 5 = n= tests until defect found P = 0.0266 There is a 2.66% percent chance that the first defective hard drive is the fifth unit tested.

## Recently Viewed Presentations

• randomly from the original population. Typically we have only one sample - of n points - observed for our variable of interest (e.g., field goal % for a team's season games) We can obtain a sample estimate (e.g., for the...
• Implementation Science: a letter from the UK Martin Eccles What's in a name? That which we call KT by any other name would smell as sweet. (Shakespear W, 1597) A study of 33 applied research funding agencies across nine countries...
• Objetivo Primordial. Estimular la innovación y propiciar la formación de futuros líderes con capacidad de identificar y solucionar problemas de las organizaciones, en sintonía permanente con las necesidades del país y la región.
• Anisotropic Diffusivity of the Prismatic surface of ice is model Independent. Natalie Bowens1, Ivan Gladich2, Amrei Oswald1,Steven Neshyba1, and Martina Roeselova2. 1University of Puget Sound, Tacoma, WA. 2Institute of Organic Chemistry and Biochemistry, Prague, Czech Republic.
• Survey Methodology Lilian Ma November 6, 2014 Three aspects 1. How questions were designed 2. How data was collected 3. How samples were drawn Probability sampling generally used. Basic Characteristics/features 1. Their purpose 2. The population they try to describe...
• The current Cisco Webex service will be replaced with Microsoft Lync in October 2013. This service replacement is a requirement in the ACES contract. The Lync on-line meeting service provides customers with the same service capabilities as WebEx but with...
• Chinese Food. Hot Pot. Hot Pot. Hot Pot Items. Duck Eggs. Toppings for Breakfast. Black Rice Cakes. Some kind of purple potato? Chopsticks. Summer melon with carrots. Fried Rice. Fish. Author: Brad Created Date: 10/30/2012 05:33:57 Title: Chinese Food Last...
• Steel from podium Painter homework problem. Get demo here have man stand at several places calculate force on each support. ... CCW rotation is positive ACT The picture below shows three different ways of using a wrench to loosen a...