Normal with mean μ and standard deviation σ

Info icon This preview shows pages 8–11. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 8

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 9
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
Image of page 10

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Chapter 9: Sampling Distributions Review Problems: 1. Based on a simple random sample of size 100, a researcher calculated the standard deviation associated with a sample proportion to be 0.08. If she increases the sample size to 400, what will be the new standard deviation associated with the sample proportion?______________ 2.
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern