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

question 68

Short Answer

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 $\mu = 27.4 \mathrm { mpg }$ and standard deviation $\sigma = 2.9 \mathrm { mpg }$ .
(a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of mpgs between $29.3$ and $23.7$ .
(c) Suppose the area under the normal curve to between $X = 29.3$ and $X = 23.7$ is $0.6419$ . Provide two interpretations of this result.

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Definitions:

Market Value

The existing market rate at which you can purchase or sell an asset or service.

Book Value

The value of an asset as shown on a company's balance sheet, calculated as the cost of the asset minus any depreciation and amortization.

Capital Balance

The amount of funds contributed by owners or shareholders to a business, plus retained earnings and reduced by any withdrawals or distributions.

Asset Revaluation

The process of adjusting the book value of an asset to reflect its current market value.