This question is a continuation of question #3. What is the probability that a sample mean calculated from a sample of 36 individuals from the Florida subdivision will have an average age between 64 and 66 years of age. As in question #3, the mean age of the population is 65 years of age, and the standard deviation is 2 years. For this problem, be sure to use the z-calculation that is for sample means, and includes the sample size: A) What is the probability that a randomly chosen individual would be less than 64.5 years of age? Show how you standardized the problem. B) If I remove the “normality statement” from the question (ie, if I assume we do not know the probability distribution of the underlying population) does this matter in completing this question? In other words, is the normality of the “underlying population” a necessary condition for completing this problem? Answer “yes” or “no”, and then in a single sentence, state why.

1. Given that: Population mean, μ=65 Population standard deviation, σ=2 Sample size, n=36

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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This question is a continuation of question #3. What is the probability that a sample mean calculated from a sample of 36 individuals from the Florida subdivision will have an average age between 64 and 66 years of age. As in question #3, the mean age of the population is 65 years of age, and the standard deviation is 2 years. For this problem, be sure to use the z-calculation that is for sample means, and includes the sample size: A) What is the probability that a randomly chosen individual would be less than 64.5 years of age? Show how you standardized the problem. B) If I remove the “normality statement” from the question (ie, if I assume we do not know the probability distribution of the underlying population) does this matter in completing this question? In other words, is the normality of the “underlying population” a necessary condition for completing this problem? Answer “yes” or “no”, and then in a single sentence, state why.

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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