Weightlifting The Atlas BodyBuilding Company (ABC)sells “starter sets” of barbells that consist of one bar, two20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard devia-tion of 0.25 pounds. The weights average the specified amounts, but the standard deviations are 0.2 pounds forthe 20-pounders and 0.1 pounds for the 5-pounders. Wecan assume that all the weights are normally distributed. a) ABC ships these starter sets to customers in twoboxes: The bar goes in one box and the six weightsgo in another. What’s the probability that the totalweight in that second box exceeds 60.5 pounds? Define your variables clearly and state any assump-tions you make. b) It costs ABC $0.40 per pound to ship the box contain-ing the weights. Because it’s an odd-shaped package, though, shipping the bar costs $0.50 a pound plusa $6.00 surcharge. Find the mean and standarddeviation of the company’s total cost for shippinga starter set.c) Suppose a customer puts a 20-pound weight at one endof the bar and the four 5-pound weights at the otherend. Although he expects the two ends to weigh thesame, they might differ slightly. What’s the probabilitythe difference is more than a quarter of a pound?

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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Weightlifting The Atlas BodyBuilding Company (ABC)
sells “starter sets” of barbells that consist of one bar, two
20-pound weights, and four 5-pound weights. The bars

weigh an average of 10 pounds with a standard devia-
tion of 0.25 pounds. The weights average the specified

amounts, but the standard deviations are 0.2 pounds for
the 20-pounders and 0.1 pounds for the 5-pounders. We
can assume that all the weights are normally distributed.

a) ABC ships these starter sets to customers in two
boxes: The bar goes in one box and the six weights
go in another. What’s the probability that the total
weight in that second box exceeds 60.5 pounds?

Define your variables clearly and state any assump-
tions you make.

b) It costs ABC $0.40 per pound to ship the box contain-
ing the weights. Because it’s an odd-shaped package,

though, shipping the bar costs $0.50 a pound plus
a $6.00 surcharge. Find the mean and standard
deviation of the company’s total cost for shipping
a starter set.
c) Suppose a customer puts a 20-pound weight at one end
of the bar and the four 5-pound weights at the other
end. Although he expects the two ends to weigh the
same, they might differ slightly. What’s the probability
the difference is more than a quarter of a pound?

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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