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Explain the Role of Area in the Normal Density Function μ=27.4mpg\mu = 27.4 \mathrm { mpg }

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Explain the Role of Area in the Normal Density Function
-The average mpg (miles per gallon) of a new model of motorcycle is known to be normally distributed with mean μ=27.4mpg\mu = 27.4 \mathrm { mpg } and standard deviation σ=2.9mpg\sigma = 2.9 \mathrm { mpg } .
(a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of mpgs between 29.329.3 and 23.723.7 .
(c) Suppose the area under the normal curve to between X=29.3X = 29.3 and X=23.7X = 23.7 is 0.64190.6419 . Provide two interpretations of this result.

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Definitions:

Bill of Material

A comprehensive list of materials, components, and instructions required to construct, manufacture, or repair a product or service.

Material Requirements

Specifications and quantities of materials needed to manufacture a product, often determined by detailed planning processes such as Material Requirements Planning (MRP).

Components

Individual parts or elements that make up a larger system, machine, or product, often interconnected to perform specific functions.

Quantity

The amount or number of a material or immaterial good considered as a unit or an aggregate.

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