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Part $1$

Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$LOADING$...$ for this problem.

Eagletrons are$$ all$-$electric automobiles produced by Mogul$$ Motors, Inc. One of the concerns of Mogul Motors is that the Eagletrons be capable of achieving appropriate maximum speeds. To monitor$$ this, Mogul executives take samples of ten Eagletrons at a time.

For each$$ sample, they determine the average maximum speed and the range of the maximum speeds within the sample.

They repeat this with $35$ samples to obtain $35$ sample means and $35$ ranges. They find that the average sample mean is $98\mathrm{.}50$ miles per$$ hour, and the average range is $3\mathrm{.}50$ miles per hour. Using these$$ results, the executives decide to establish an$$ R$-$chart. They would like this chart to be established so that when it shows that the range of a sample is not within the control$$ limits$,$ there is only approximately a $0\mathrm{.}0027$ probability that this is due to natural variation.

The control limits for the chart based on the above requirement for the given information$$ are:

Part $2$

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enter your response here miles per hour $($round the reponse to three decimal$$ places$).$