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?
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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 19PPS
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Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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Question
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
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
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 arenormally distributed.
the 20-pounders and 0.1 pounds for the 5-pounders. We
can assume that all the weights are
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?
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.
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,
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?
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?
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