Answered: leading magazine (like Barron's)…

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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Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 32 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 32 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 55 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 31.7.
P(X > 31.7) = (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n=55n=55 is randomly selected with a mean greater than 31.7.
P(M > 31.7) = (Enter your answers as numbers accurate to 4 decimal places.)

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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