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Unformatted text preview: “With that said, so that we err on the side of caution, we will say that the distribution of the sample mean is approximately normal provided that the sample size is greater than or equal to 30, if the distribution of the population is unknown or not normal.” Chapter 9: Sampling Distributions Shape, Center and Spread of Population Distribution of the Sample Means Shape Center Spread Normal with mean, μ and standard deviation, σ Regardless of sample size, n, distribution of x-bar is normal μ x-bar = μ σ σ x-bar = ------- √ n Population is not normal with mean, μ and standard deviation, σ As sample size, n, increases, the distribution of x-bar becomes approximately normal μ x-bar = μ σ σ x-bar = ------- √ n Summary of Distribution of x Chapter 9: Sampling Distributions Example 1: The height of all 3-year-old females is approximately normally distributed with μ = 38.72 inches and σ = 3.17 inches. Compute the probability that a simple random sample of size n = 10 results in a sample mean greater than 40 inches. Example 2: We’ve been told that the average weight of giraffes is 2400 pounds with a standard deviation of 300 pounds. We’ve measured 50 giraffes and found that the sample mean was 2600 pounds. Is our data consistent with what we’ve been told? Example 3: Young women’s height is distributed as a N(64.5, 2.5), What is the probability that a randomly selected young woman is taller than 66.5 inches? Example 4: Young women’s height is distributed as a N(64.5, 2.5), What is the probability that an SRS of 10 young women is greater than 66.5 inches? Example 5: The time a technician requires to perform preventive maintenance on an air conditioning unit is governed by the exponential distribution (similar to curve a from “in Action” slide). The mean time is μ = 1 hour and σ = 1 hour. Your company has a contract to maintain 70 of these units in an apartment building. In budgeting your technician’s time should you allow an average of 1.1 hours or 1.25 hours for each unit? Summary: The sample mean is a random variable with a distribution called the sampling distribution ● If the sample size n is sufficiently large (30 or more is a good rule of thumb), then this distribution is approximately normal ● The mean of the sampling distribution is equal to the mean of the population ● The standard deviation of the sampling distribution is equal to σ / √ n Homework: Day 1: pg 595-6; 9.31-4 Day 2: pg 601-4; 9.35, 36, 38, 42-44 Chapter 9: Sampling Distributions Chapter 9: Review Objectives: Students will be able to: Summarize the chapter • Define a sampling distribution • Contrast bias and variability • Describe the sampling distribution of a sample proportion (shape, center, and spread) • Use a Normal approximation to solve probability problems involving the sampling distribution of a sample proportion • Describe the sampling distribution of a sample mean • State the central limit theorem • Solve probability problems involving the sampling distribution of a sample mean Define the vocabulary used Know and be able to discuss all sectional knowledge objectives Complete all sectional construction objectives Successfully answer any of the review exercises Vocabulary: None new Homework: pg 607 – 609; 9.47, 49-53, 56, 58 Chapter 9:...
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