Answered: Based on a recent report, the cost 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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Question

Based on a recent report, the cost of healthcare is $8,086 per person in the United States. Suppose that this is the population mean and the population standard deviation is $2,500. A research firm will take a sample of 15 people to investigate the nature of their health expenditures.

a) What is the probability the sample mean amount of healthcare expenditure will be greater than $9,000?

b) What is the probability the sample mean will be within $500 of the population mean?

c) What is the probability the sample mean will be within $1,000 of the population mean?

Note: Since the sample size is smaller than 30, theoretically, the central limit theorem does not apply and therefore we must make the assumption that healthcare cost per person follows normal distribution.

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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