Answered: In the 1992 presidential election,…

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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In the 1992 presidential election, Alaska's 40 election districts averaged 2023 votes per district for President Clinton. The standard deviation was 555. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.

a. What is the distribution of X? X ~ N( , )

b. Is 2023 a population mean or a sample mean? Select an answer Population Mean or Sample Mean?

c. Find the probability that a randomly selected district had fewer than 1989 votes for President Clinton?

d. Find the probability that a randomly selected district had between 1938 and 2139 votes for President Clinton?

e. Find the first quartile for votes for President Clinton? Round your answer to the nearest whole number.

Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 6 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N( , )

b. If one car is randomly chosen, find the probability that it is traveling more than 73 mph?

c. If one of the cars is randomly chosen, find the probability that it is traveling between 70 and 76 mph?

d. 72% of all cars travel at least how fast on the freeway? mph.

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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