In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (?Genessy v. Digital Equipment Corp?.)?. ?The injury awarded about $3.5 million for pain and suffering but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a “normative” group of 27 similar cases and specified a reasonable award as one within two standard deviations of the mean of the awards in the 27 cases. The 27 awards were (in $1000s) 37, 60, 75, 115, 135, 140, 149, 150, 238, 290, 340, 410, 600, 750, 750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250, 1576, 1700, 1825, and 2000, from which ,?xi = 20,179, ?x2i = 24,657,511 . What is the maximum possible amount that could be awarded under the twostandard-deviation rule?

Answer : Step 1 : Given the injury awarded about $3.5 million for pain and suffering but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a “normative” group of 27 similar cases and specified a reasonable award as one within two standard deviations of the mean of the awards in the 27 cases. The 27 awards were (in $1000s). Here n=27 Then the data is 37, 60, 75, 115, 135, 140, 149, 150, 238, 290, 340, 410, 600, 750, 750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250, 1576, 1700, 1825, and 2000, from which ,x = 20,179 and i x2i = 24,657,511 So we have to find the maximum possible amount that could be awarded under the two standard-deviation rule. We know that x i 20,179 and n=27. So we have to find mean. The formula of the mean is xi x = n Substitute the value i = 20,179 and n=27. 20,179 x = 27 x = 747.3703 Therefore mean is 747.3703 Then we need to find the standard deviation....