Answered: A survey found that women's heights…

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 survey found that women's heights are normally distributed with mean

63.463.4

in. and standard deviation

2.32.3

in. The survey also found that men's heights are normally distributed with mean

68.368.3

in. and standard deviation

3.83.8

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

5656

in. and a maximum of

6464

in. Complete parts (a) and (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?

The percentage of men who meet the height requirement is

nothing%.

(Round to two decimal places as needed.)

Since most men

▼

do not meet

meet

the height requirement, it is likely that most of the characters are

▼

women.

men.

b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

The new height requirements are a minimum of

nothing

in. and a maximum of

nothing

in.

(Round to one decimal place as needed.)

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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