Question

Fuel economy estimates for automobiles built one year predicted a mean of 27.2 mpg and a standard deviation of 4.8 mpg for highway driving. Assume that a Normal model can be applied.
a. Draw the model for auto fuel economy. Clearly label it, showing what the 68-95-99.7 Rule predicts.

Answer 1

Answer:

And the figure attached illustrate the limits for this case:

Between one deviation from the mean the limits are 22.4 and 32

Between two deviations from the mean the limits are 17.6 and 36.8

Between three deviations from the mean the limits are 12.8 and 41.6

Step-by-step explanation:

Previous concepts

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the fuel economu estimates.

From the problem we have the mean and the standard deviation for the random variable X. $E(X)=27.2, Sd(X)=4.8$

So we can assume $\mu=27.2 , \sigma=4.8$

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

And the figure attached illustrate the limits for this case:

Between one deviation from the mean the limits are 22.4 and 32

Between two deviations from the mean the limits are 17.6 and 36.8

Between three deviations from the mean the limits are 12.8 and 41.6