Suppose that the random variable X has a distribution with a density curve that looks like the following: The sampling distribution of the mean of.

Slides:

Advertisements

Similar presentations

Sampling Distributions

Advertisements

The Normal Distribution

Chapter 6 – Normal Probability Distributions

Binomial Distributions

Normal Distribution * Numerous continuous variables have distribution closely resemble the normal distribution. * The normal distribution can be used to.

Continuous Random Variables and Probability Distributions

1 BA 275 Quantitative Business Methods Statistical Inference: Confidence Interval Estimation Introduction Estimating the population mean  Examples Office.

Chapter 11: Random Sampling and Sampling Distributions

Copyright © Cengage Learning. All rights reserved. 6 Normal Probability Distributions.

Chapter 6 The Normal Distribution Section 6-3 The Standard Normal Distribution.

AP Statistics Chapter 9 Notes.

Normal Approximation Of The Binomial Distribution:

A P STATISTICS LESSON 2 – 2 STANDARD NORMAL CALCULATIONS.

Section 6.3 Finding Probability Using the Normal Curve HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.

Sampling Distribution of a sample Means

Normal Distributions.

Rule of sample proportions IF:1.There is a population proportion of interest 2.We have a random sample from the population 3.The sample is large enough.

Modular 11 Ch 7.1 to 7.2 Part I. Ch 7.1 Uniform and Normal Distribution Recall: Discrete random variable probability distribution For a continued random.

AP STATISTICS LESSON SAMPLE MEANS. ESSENTIAL QUESTION: How are questions involving sample means solved? Objectives:  To find the mean of a sample.

BUS304 – Chapter 6 Sample mean1 Chapter 6 Sample mean  In statistics, we are often interested in finding the population mean (µ):  Average Household.

Sample Variability Consider the small population of integers {0, 2, 4, 6, 8} It is clear that the mean, μ = 4. Suppose we did not know the population mean.

The Standard Normal Distribution Section 5.2. The Standard Score The standard score, or z-score, represents the number of standard deviations a random.

Chapter 9 Day 1. Parameter and Statistic  Parameter – a number that describes a population, usually impossible to find  Statistic – A number described.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

An opinion poll asks, “Are you afraid to go outside at night within a mile of your home because of crime?” Suppose that the proportion of all adults who.

Discrete and Continuous Random Variables. Yesterday we calculated the mean number of goals for a randomly selected team in a randomly selected game.

Chapter 6 The Normal Distribution Section 6-3 The Standard Normal Distribution.

Chapter 7 The Normal Probability Distribution 7.3 Applications of the Normal Distribution.

What does a population that is normally distributed look like? X 80  = 80 and  =

1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.

Sampling Distribution, Chp Know the difference between a parameter and a statistic.

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

MATH Section 4.4.

Chapter 9 Sampling Distributions 9.1 Sampling Distributions.

Empirical Rule 68% 95% 99.7% % RULE Empirical Rule—restated 68% of the data values fall within 1 standard deviation of the mean in either direction.

Topic 8: Sampling Distributions

Chapter 7 The Normal Probability Distribution

Inference for the Mean of a Population

Chapter 6 Continuous Probability Distribution

Understanding Sampling Distributions: Statistics as Random Variables

Applications…….

Chapter 9.3: Sample Means Mr. Lynch AP Statistics.

CHAPTER 9 Sampling Distributions

5.2 Normal Distributions: Finding Probabilities

The Normal Curve and Sampling Error

The Normal Distribution

Chapter Six Normal Curves and Sampling Probability Distributions

Distribution of the Sample Means

Chapter 5 Normal Probability Distributions

Binomial Distributions

Lecture 13 Sections 5.4 – 5.6 Objectives:

Sample vs Population comparing mean and standard deviations

Chapter 5: Sampling Distributions

Sampling Distributions

Chapter 5 Sampling Distributions

Sections 5-1 and 5-2 Quiz Review Warm-Up

Sampling Distribution

Sampling Distribution

Warm-up A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation.

Chapter 5 Normal Probability Distributions

Warmup To check the accuracy of a scale, a weight is weighed repeatedly. The scale readings are normally distributed with a standard deviation of

Inference for Distributions

9.3 Sample Means.

The Practice of Statistics

Sampling Distributions

The Practice of Statistics

Use the graph of the given normal distribution to identify μ and σ.

Sample Means Section 9.3.

A note about z-scores: All z-scores do not follow a Normal distribution. A z-score simply tells how many standard deviations a value is from the mean,

Presentation transcript:

Suppose that the random variable X has a distribution with a density curve that looks like the following: The sampling distribution of the mean of a random sample of 350 observations from this distribution will have a density curve that looks most like which of the following? Left Middle Right

Suppose that the random variable X has a distribution with a density curve that looks like the following: The sampling distribution of the mean of a random sample of 350 observations from this distribution will have a density curve that looks most like which of the following? Left Middle Right

Incomes in a certain town are strongly right skewed with mean $36,000 and standard deviation $7000. A random sample of 75 households is taken. What is the standard deviation of the sample mean? It is It is $7000

Impossible to determine without more information. The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean that varies slightly from year to year and standard deviation 6.0. You plan to take an SRS of size n of the students who took the ACT exam this year and compute the mean score of the students in your sample. You will use this to estimate the mean score of all students this year. In order for the standard deviation of to be no more than 0.1, how large should n be? At least 60. At least 3600. Impossible to determine without more information.

Incomes in a certain town are strongly right skewed with mean $36,000 and standard deviation $7,000. A random sample of 75 households is taken. What is the probability that the sample mean is greater than $37,000? 0.4432 0.1080

Answers C,C,A,B,B