Answered: 3% of a country’s voters are…

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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53% of a country’s voters are dissatisfied with the direction of the government. Suppose a SRS of 50 voters was selected and asked if they were dissatisfied with the government. Let the variable X denote the number of dissatisfied voters selected out of 50. Please answer the following questions. a) How is the variable X distributed? b) Find the probability that at most 29 dissatisfied voters are selected in this sample . c) Find the probability that at least 30 dissatisfied voters are selected in this sample d)Find the probability that exactly 30 are selected in this sample e) Find the probability that between 20 and 25 dissatisfied voters inclusive are selected in this sample. f) Find the mean number of dissatisfied voters of samples of size 50 taken from this population g) Find the variance and standard deviation of the variable X.

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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