Answered: Suppose you choose a random sample of…

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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Suppose you choose a random sample of size 100 from a large population of household incomes, which might or might not be normally distributed. If the population mean and population standard deviation are, respectively, $50,000 and $15,000, which of the following is at least approximately true because of the central limit theorem?

a. The probability that the sample mean will be between $48,500 and $51,500 is above 0.99.

b. The probability that the sample mean will be between $48,500 and $51,500 is about 0.95.

c. The probability that the sample mean will be between $47,000 and $53,000 is about 0.95.

d. The probability that the sample mean will be between $47,000 and $53,000 is about 0.68.

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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