Suppose a sample of 50 MP3 players is drawn randomly from a population of MP3 players and the weight, x, of each MP3 player is recorded. Prior experience has shown that the weight of a single MP3 player has a mean of 6 ounces and a standard deviation of 2.5 ounces. a) Describe the shape of the sample mean : b) What is the mean and standard deviation of the sampling distribution of ? c) What is the probability that the sample has a mean weight of less than 5 ounces?

Suppose a sample of 50 MP3 players is drawn randomly from a population of MP3 players and the weight, x, of each MP3 player is recorded. Prior experience has shown that the weight of a single MP3 player has a mean of 6 ounces and a standard deviation of 2.5 ounces. a) Describe the shape of the sample mean : b) What is the mean and standard deviation of the sampling distribution of ? c) What is the probability that the sample has a mean weight of less than 5 ounces?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

a) Describe the shape of the sample mean :

b) What is the mean and standard deviation of the sampling distribution of ?

c) What is the probability that the sample has a mean weight of less than 5 ounces?

d) How would the sampling distribution of ?̅ change if the sample size, n , were increased from 50 to 100?

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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d) How would the sampling distribution of ?̅ change if the sample size, n , were increased from 50 to 100?

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