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

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.