Answered: Assume that the heights of American men…

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

Assume that the heights of American men are normally distributed with a mean of 69.1 inches and a standard deviation of 3.3 inches.

Of the 44 presidents elected from 1789 through 2016, 19 were 6'0" or taller. The proportion of all men that will be taller than 6'0" is 0.18976.

If the 44 presidents could be considered a random sample of 44 American men, how many standard deviations above the mean would an observation of 19 out of 44 of the men being 6'0" tall or taller be? (Hint: We can consider the number of men 6'0" tall or taller in a random sample of 44 men to be a binomial random variable where the probability of selecting a man 6'0" tall or taller is the proportion of American men 6'0" tall or taller. Round your answer to two decimal places.)

Z = ?

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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