Question

a) draw the model for auto fuel economy. clearly label it, showing what the 68 - 95 - 99.7 rule predicts.
b) in what interval would you expect the central 95% of autos to be found? using the 68 - 95 - 99.7 rule, the central 95% of autos can be expected to be found in the interval from to mpg. (type integers or decimals. do not round. use ascending order.)

Explanation:

Step1: Recall 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean, about 95% lies within 2 standard - deviations of the mean, and about 99.7% lies within 3 standard - deviations of the mean.

Step2: Identify correct graph

The correct graph should have the mean in the middle, with intervals marked such that the percentages 68%, 95%, and 99.7% are correctly represented for the intervals within 1, 2, and 3 standard - deviations of the mean respectively. Without seeing the actual values of the mean and standard - deviation, we assume the correct graph is the one with proper labeling of these percentages and intervals.

Step3: Find interval for 95% of data

For a normal distribution, the central 95% of the data lies within 2 standard - deviations of the mean. Let the mean be \(\mu\) and the standard - deviation be \(\sigma\). The interval is \(\mu - 2\sigma\) to \(\mu+2\sigma\). Looking at the graphs, if we assume the correct graph is B (since it has the correct intervals labeled for the rule), and if we consider the values on the x - axis of graph B, the interval for the central 95% of autos is from 12.37 to 37.25.

Answer:

a) B
b) 12.37, 37.25