Answered: Suppose a sample of 50 MP3 players is…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

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?

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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