Concrete is loaded into trucks for a large construction project according to a normal distribution. The mean amount loaded is 230 cubic feet with a standard deviation of 7 cubic feet. Concrete trucks are rated by the number of cubic yards they can carry, and 9 cubic yards is a common maximum load. Hence the expression “the whole nine yards.”a. What proportion of the trucks will be loaded with between 220 and 240 cubic feet?b. What proportion of trucks are loaded with more concrete than the 9 cubic yard maximum. (3 feet = 1 yard)c. 235 cubic feet is what percentile load?d. If a particular job requires at least 220 cubic yards of concrete, what is the probability there will not be enough concrete in a single truck?

Given that: Population mean, μ=230 Population standard deviation, σ=7

Answered: Concrete is loaded into trucks for a…

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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Concrete is loaded into trucks for a large construction project according to a normal distribution. The mean amount loaded is 230 cubic feet with a standard deviation of 7 cubic feet. Concrete trucks are rated by the number of cubic yards they can carry, and 9 cubic yards is a common maximum load. Hence the expression “the whole nine yards.”

a. What proportion of the trucks will be loaded with between 220 and 240 cubic feet?
b. What proportion of trucks are loaded with more concrete than the 9 cubic yard maximum. (3 feet = 1 yard)
c. 235 cubic feet is what percentile load?
d. If a particular job requires at least 220 cubic yards of concrete, what is the probability there will not be enough concrete in a single truck?

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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