Question

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 103.50 miles per​ hour, and the average range is 3.50 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 0.0027 probability that this is due to natural variation.

Answer 1

Upper control limit =6.058

Lower control limit= 0.442

Explanation:

Mogul executives takes samples of n=8 Eagletrons at a time

Their average range = 3.25mph

From table value for n=8

D4 =1.864

D3 = 0.136

Control limit (r)= 3.25

Upper control limit = 1.864×3.25=6.058

Lower control limit = 0.136×3.25=0.442