22. The Fizzy Company produces six-packs of soda cans.Each can is supposed to contain at least 12 ouncesof soda. If the total weight in a six-pack is less than72 ounces, Fizzy is fined $100 and receives no salesrevenue for the six-pack. Each six-pack sells for$3.00. It costs Fizzy $0.02 per ounce of soda put inthe cans. Fizzy can control the mean fill rate of itssoda-filling machines. The amount put in each canby a machine is normally distributed with standarddeviation 0.10 ounce.a. Assume that the weight of each can in a six-packhas a 0.8 correlation with the weight of the othercans in the six-pack. What mean fill quantitymaximizes expected profit per six-pack? Trymean fill rates from 12.00 to 12.35 in incrementsof 0.05.b. If the weights of the cans in the six-pack areprobabilistically independent, what mean fillquantity maximizes expected profit per six-pack?Try the same mean fill rates as in part a.c. How can you explain the difference in the answersto parts a and b?
22. The Fizzy Company produces six-packs of soda cans.Each can is supposed to contain at least 12 ouncesof soda. If the total weight in a six-pack is less than72 ounces, Fizzy is fined $100 and receives no salesrevenue for the six-pack. Each six-pack sells for$3.00. It costs Fizzy $0.02 per ounce of soda put inthe cans. Fizzy can control the mean fill rate of itssoda-filling machines. The amount put in each canby a machine is normally distributed with standarddeviation 0.10 ounce.a. Assume that the weight of each can in a six-packhas a 0.8 correlation with the weight of the othercans in the six-pack. What mean fill quantitymaximizes expected profit per six-pack? Trymean fill rates from 12.00 to 12.35 in incrementsof 0.05.b. If the weights of the cans in the six-pack areprobabilistically independent, what mean fillquantity maximizes expected profit per six-pack?Try the same mean fill rates as in part a.c. How can you explain the difference in the answersto parts a and b?
22. The Fizzy Company produces six-packs of soda cans.Each can is supposed to contain at least 12 ouncesof soda. If the total weight in a six-pack is less than72 ounces, Fizzy is fined $100 and receives no salesrevenue for the six-pack. Each six-pack sells for$3.00. It costs Fizzy $0.02 per ounce of soda put inthe cans. Fizzy can control the mean fill rate of itssoda-filling machines. The amount put in each canby a machine is normally distributed with standarddeviation 0.10 ounce.a. Assume that the weight of each can in a six-packhas a 0.8 correlation with the weight of the othercans in the six-pack. What mean fill quantitymaximizes expected profit per six-pack? Trymean fill rates from 12.00 to 12.35 in incrementsof 0.05.b. If the weights of the cans in the six-pack areprobabilistically independent, what mean fillquantity maximizes expected profit per six-pack?Try the same mean fill rates as in part a.c. How can you explain the difference in the answersto parts a and b?
22. The Fizzy Company produces six-packs of soda cans. Each can is supposed to contain at least 12 ounces of soda. If the total weight in a six-pack is less than 72 ounces, Fizzy is fined $100 and receives no sales revenue for the six-pack. Each six-pack sells for $3.00. It costs Fizzy $0.02 per ounce of soda put in the cans. Fizzy can control the mean fill rate of its soda-filling machines. The amount put in each can by a machine is normally distributed with standard deviation 0.10 ounce. a. Assume that the weight of each can in a six-pack has a 0.8 correlation with the weight of the other cans in the six-pack. What mean fill quantity maximizes expected profit per six-pack? Try mean fill rates from 12.00 to 12.35 in increments of 0.05. b. If the weights of the cans in the six-pack are probabilistically independent, what mean fill quantity maximizes expected profit per six-pack? Try the same mean fill rates as in part a. c. How can you explain the difference in the answers to parts a and b?
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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