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Unformatted text preview: (7.3, 7.5) Sampling Distributions It is often of interest to know the mean of a population however the actual mean of a population is often difficult or impossible to obtain. One way to estimate the population mean is to take a sample and find the sample average (which we will refer to as ? ). When we have a large sample ( >30 is typical), the sample average will follow a normal distribution. This is known as the Central Limit Theorem. Dice Example: Distribution and parameters of ? Example : Chips Ahoy is famous for it s slogan 1,000 chips delicious. In fact, they guarantee that if your box of Chips Ahoy cookies do not have at least 1,000 chips, they will give you a full refund and a free case of cookies. A box of Chips Ahoy cookies has 80 cookies. The number of chocolate chips in each cookie follows a Poisson distribution with an average of 13 chips. Let C be the number of chocolate chips in a box of Chips Ahoy cookies. What are the distribution and parameters of C? You decide to buy a box of Chips Ahoy cookies. What is the probability you get a free case? If all boxes of cookies are independent and you buy 20 boxes, how many do you expect to have less than 1,000 chips? Sometimes we take a sample and it is not the average we are looking for, it is the sum. Luckily, the Central Limit Theorem will take that into account too. The sum of a sample will also follow a Normal distribution. Distribution and parameters of ? Example: The weight of an average adult has a mean of 150 pounds with a standard deviation of 50 pounds. The elevator at a local hotel holds a maximum weight of 5,000 pounds. Let W be the total weight of 30 people (all independent) that step into this elevator. What are the distribution and parameters of W? What is the probability the elevator breaks down? This elevator is really busy and carries 30 people in each load for the next 65 loads. Each elevator run takes 2 minutes and it takes 15 additional minutes to fix the elevator that breaks down. How much time do you expect it to have taken these 65 loads to complete? Sometimes we are interested in the proportion of a population that has a certain characteristic. Again, the proportion of a sample follows a normal distribution. We will use ? to denote the sample proportion we will use to estimate the population proportion. Distribution and parameters of ? In the year 1800 the election between T homas Jefferson and Aaron Burr resulted in over 36 ties and had to go to a statebystate vote before Jefferson was finally elected president. You are given the statebystate votes (50 total) and are to count them and find the proportion of Jefferson votes among the states. Let J be the proportion of Jefferson votes in the 50 states....
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 MARTIN

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