Question

In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury 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 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below. 31 60 75 115 135 140 149 150 236 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1576 1700 1825 2000 What is the maximum possible amount that could be awarded under the "2-standard deviations rule"? (Round all intermediate calculations and the answer to three decimal places.) (in thousands of $)

          In 1997 a woman sued a computer keyboard manufacturer, charging
that her repetitive stress injuries were caused by the keyboard
(Genessey v. Digital Equipment Corporation). The jury
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
2 standard deviations of the mean of the awards in the 27 cases.
The 27 award amounts (in thousands of dollars) are in the table
below.
31
60
75
115
135
140
149
150
236
290
340
410
600
750
750
750
1050
1100
1139
1150
1200
1200
1250
1576
1700
1825
2000
What is the maximum possible amount that could be awarded under
the "2-standard deviations rule"? (Round all intermediate
calculations and the answer to three decimal places.)
  (in thousands of $)

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Added by Joseph V.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Rabia Sarwar

09/02/2023

Step 1

The award amounts are: 31, 60, 75, 115, 135, 140, 149, 150, 236, 290, 340, 410, 600, 750, 750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250, 1576, 1700, 1825, 2000. First, sum all the award amounts: \[ 31 + 60 + 75 + 115 + 135 + 140 + 149 + 150 + 236 + Show more…

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In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury 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 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below. 31 60 75 115 135 140 149 150 236 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1576 1700 1825 2000 What is the maximum possible amount that could be awarded under the "2-standard deviations rule"? (Round all intermediate calculations and the answer to three decimal places.) (in thousands of $)

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Transcript

00:01 So in this question we have to calculate the maximum possible awards amount could be award for two standard generation.

00:14 Here the award number award numbers in thousand in dollars.

00:22 So we write the award number is 35 60 75 1 1 5 so 1 1 5 1 3 5 1 40 1 49 1 50 2 32 2 90 3 40 4 10 600 750 750 750 so 1 0 5 0 1 1 3 9 1100 1 1 5 0 1200 1200 1250 so last one is 1 5 7 6 1700 1825 and 2000.

01:24 So first we calculate the mean and standard deviation.

01:31 Calculate mean and standard deviation.

01:51 So mean is equal to plus all the values so 35 plus 60 plus 75 so divide 2000 or divided by 27 values so mean is equal to 941.

02:16 Then we calculate the standard deviation.

02:20 So standard deviation is equal to sum of x i minus mean whole square divided by n.

02:35 So this one is under root.

02:39 So it represents sum.

02:46 It represents each individual value.

02:53 So all values like 60 35 6 35 60 individual value and this one is mean value.

03:03 Mean value this one is 941.

03:06 And next at last number number of values number of values.

03:17 So we know about so putting all we know that 941 x i all values 1 to 1 and n is 27.

03:37 So under root standard deviation.

03:41 So we find the standard deviation all the plus value and 94.

03:46 So it's equal to 14151676...

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