A woman sued a computer keyboard manufacturer charging that

A woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard. 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) 36, 60, 72, 111, 139, 144, 147, 153, 238, 290, 340, 410, 600, 750, 750, 753, 1050, 1100, 1139, 1150, 1200, 1200, 1250, 1578, 1700, 1825, and 2000, from which Exi = 20,185, Exi2 = 24,669,459. what is the maximum possible amount that could be awarded under the two-standard-deviation rule? (Round your answer to the nearest whole number.) X thousand dollars

Solution

Just go through this answer :

You must find the mean and standard deviation of the 27 cases.
Number of cases 27
To find the mean, add all of the observations and divide by 27
Mean 747.2222
Squared deviations
(39-(747.2222))^2 = (-708.2222)^2 = 501578.716
(60-(747.2222))^2 = (-687.2222)^2 = 472274.3827
(75-(747.2222))^2 = (-672.2222)^2 = 451882.716
(115-(747.2222))^2 = (-632.2222)^2 = 399704.9383
(135-(747.2222))^2 = (-612.2222)^2 = 374816.0494
(140-(747.2222))^2 = (-607.2222)^2 = 368718.8272
(149-(747.2222))^2 = (-598.2222)^2 = 357869.8272
(150-(747.2222))^2 = (-597.2222)^2 = 356674.3827
(236-(747.2222))^2 = (-511.2222)^2 = 261348.1605
(290-(747.2222))^2 = (-457.2222)^2 = 209052.1605
(340-(747.2222))^2 = (-407.2222)^2 = 165829.9383
(410-(747.2222))^2 = (-337.2222)^2 = 113718.8272
(600-(747.2222))^2 = (-147.2222)^2 = 21674.3827
(750-(747.2222))^2 = (2.7778)^2 = 7.716
(750-(747.2222))^2 = (2.7778)^2 = 7.716
(750-(747.2222))^2 = (2.7778)^2 = 7.716
(1050-(747.2222))^2 = (302.7778)^2 = 91674.3827
(1100-(747.2222))^2 = (352.7778)^2 = 124452.1605
(1139-(747.2222))^2 = (391.7778)^2 = 153489.8272
(1150-(747.2222))^2 = (402.7778)^2 = 162229.9383
(1200-(747.2222))^2 = (452.7778)^2 = 205007.716
(1200-(747.2222))^2 = (452.7778)^2 = 205007.716
(1250-(747.2222))^2 = (502.7778)^2 = 252785.4938
(1572-(747.2222))^2 = (824.7778)^2 = 680258.3827
(1700-(747.2222))^2 = (952.7778)^2 = 907785.4938
(1825-(747.2222))^2 = (1077.7778)^2 = 1161604.9383
(2000-(747.2222))^2 = (1252.7778)^2 = 1569452.1605
Add the squared deviations and divide by 26

Variance (using n-1) = 9568914.6667/26
Variance 368035.1795
Standard deviation (using n-1) = sqrt(variance) = 606.659

Mean = $747.22 (thousands)
SD = 606.659

Mean + 2 SD = 747.22+ 2(606.659) = 1,960.54 (in thousands of dollars)