A gas station earns $2.500 in revenue for each gallon of regular gas it sells, $2.550 for each gallon of midgrade gas, and $2.600 for each gallon of premium gas. Let X1, X2, and X3 denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X1, X2, and X3 have means μ1=1500, μ2=500, and μ3=300, and standard deviations σ1=180, σ2=90, and σ3=40, respectively.1) Find the mean daily revenue. 2) Assuming X1, X2, and X3 to be independent, find the standard deviation of the daily revenue. (Round the final answer to three decimal places.)

1. The mean daily revenue for the gas station is $5,805. 2. The standard deviation of the daily…

Answered: A gas station earns $2.500 in revenue…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.8: Joint And Combined Variation

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A gas station earns $2.500 in revenue for each gallon of regular gas it sells, $2.550 for each gallon of midgrade gas, and $2.600 for each gallon of premium gas. Let X₁, X₂, and X₃ denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X₁, X₂, and X₃ have means μ₁=1500, μ₂=500, and μ₃=300, and standard deviations σ₁=180, σ₂=90, and σ₃=40, respectively.

1) Find the mean daily revenue.
2) Assuming X₁, X₂, and X₃ to be independent, find the standard deviation of the daily revenue. (Round the final answer to three decimal places.)

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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