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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The Answer of 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.

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

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