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:

Standard Hours

The set amount of time expected to complete a job or task, often used for planning and assessing the efficiency of operations.

Volume Variance

The difference between the budgeted volume of production and the actual volume, which affects the fixed overhead costs.

Direct Labor-Hours

A measure of the total hours worked by employees who are directly involved in the production process of a company's products or services.

Fixed Manufacturing Overhead

The portion of manufacturing overhead costs that do not vary with the level of production or sales, such as factory rent.