1. Use the dataset labeled Company 1 and Company 2 down below and answer the following questions:

1. Make a histogram of the weights for each company. Comment on the distributions.
2. Calculate the confidence intervals for the mean of plates made by company 1 versus company 2. Do not worry about degrees of freedom; you can use Z=1.96 for your calculations.
3. The International Weightlifting Federation (IWF) requires that mean weight of plates used in the Olympic Games and other competitions be within .1 kg of the stated weight with 95% confidence. Can either company meet this requirement?
4. Suppose a contract with the IWF is worth $10,000,000. A company can upgrade their manufacturing facility and eliminate outliers. Each upgrade costs $2,500,000 and eliminates one outlier. When an outlier is eliminated, recalculate the confidence interval for the mean without it included. For the company or companies that failed to meet the standard for part (c) of this question, is it profitable to make these upgrades? Explain.

Company 1:

Company 2:

17.780819976648 19.226105386657 19.760915302727 19.762038815416 19.768539222306 19.769731627903 19.771364071808 19.775686400161 19.778416363799 19.779862292217 19.783919778107 19.791767848406 19.79467524218 19.807369571378 19.810440589782 19.820084152955 19.821879894848 19.829484376103 19.843196573599 19.852804941577 Stated Weight Actual Weight 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 19.854420930086 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 19.855412970489 19.868849940412 19.868850695769 19.874128258378 19.875213633228 19.876400272867 19.878895555655 19.880764903913 19.898388077135 19.899637159994 19.900248234856 19.902474494351 19.916631271256 19.91836667123 19.919563810606 19.925835845918 19.932603224688 19.937618826554 19.940483728491 19.952008158342 19.960191570696 19.966399052881 19.971487078761 19.975117310741 19.980704571086 19.981334692219 20.005450946738 20.009227204313 20.01261803118 20.015546045769 20.016178468223 20.022988209927 20.024705030489 20.025027340338 20.030841084733 20.04181135738 20.044428165377 20.044925661714 20.048921539018 20.048959778252 20.051933140019 20.062846928986 20.065757756548 20.070741735804 20.072247759964 20.078947731703 20.081382874002 20.085773412207 20.088741030918 20.09118645181 20.093233387125 20.102275047671 20.106831062998 20.123765395894 20.13030569307 20.130753490213 20.141885955943 20.14218383035 20.142755172783 20.148641619591 20.154639626492 20.163831293787 20.177500276537 20.184519232016 20.187377109666 20.188895705149 20.195997281323 20.203554190026 20.203985639679 20.210046885233 20.213167019793 20.215614294569 20.218406254291 20.219187358543 20.226215548629 20.227022282728 20.230176795325 21.075724526062 22.059187362402 Stated weight actual weight 20kg 17.404082900994 20kg 18.262151568893 20kg 17.396012400322 20kg 19.130773624794 20kg 19.231598141749 20kg 19.763183456686 20kg 19.764649690775 20kg 19.767694678039 20kg 19.769343458739 20kg 19.779045247658 20kg 19.791656125774 20kg 19.794417269807 20kg 19.795285715149 20kg 19.800621440863 20kg 19.801161703397 20kg 19.812920669061 20kg 19.81830019184 20kg 19.818596088735 20kg 19.825150073575 20kg 19.842386296258 20kg 19.842793147146 20kg 19.846012970075 20kg 19.857181247772 20kg 19.857549628304 20kg 19.860930514417 20kg 19.87433871758 20kg 19.879278937034 20kg 19.880163061105 20kg 19.884399529471 20kg 19.892496029115 20kg 19.893958886815 20kg 19.900930976037 20kg 19.904978483508 20kg 19.909965315239 20kg 19.916453716499 20kg 19.922159011391 20kg 19.924236015167 20kg 19.931181467392 20kg 19.932611766089 20kg 19.94312827711 20kg 19.955417695826 20kg 19.972572407899 20kg 19.973125145954 20kg 19.99134343415 20kg 19.997291206864 20kg 19.998345960438 20kg 20.003600248474 20kg 20.005912683873 20kg 20.009474557379 20kg 20.016841330227 20kg 20.017022457427 20kg 20.017706123226 20kg 20.018583549193 20kg 20.018694521649 20kg 20.019536627357 20kg 20.023855435906 20kg 20.034615564596 20kg 20.040521958364 20kg 20.041343960647 20kg 20.056751914604 20kg 20.058750718863 20kg 20.066673548005 20kg 20.067052187889 20kg 20.073760520267 20kg 20.085183390656 20kg 20.088371501066 20kg 20.095858755121 20kg 20.100269512457 20kg 20.104638543576 20kg 20.12307903952 20kg 20.124663798255 20kg 20.130243295275 20kg 20.139747676376 20kg 20.147677604248 20kg 20.158732053527 20kg 20.160363276699 20kg 20.16310017769 20kg 20.169468678004 20kg 20.171866311075 20k 20.175633789093 20kg 20.179858417394 20kg 20.182060105395 20kg 20.188086712093 20kg 20.190524057499 20kg 20.191450753385 20kg 20.205278653376 20kg 20.205291363676 20kg 20.207000831464 20kg 20.208905408291 20kg 20.21445462565 20kg 20.222234385737 20kg 20.2302877994 20kg 20.231835513941 20kg 20.237999799474 20kg 20.241179178538 20kg 20.251525726458 20kg 22.315150575791 20kg 21.461207260986 20kg 21.740637667652 20kg 22.253561561708 17.780819976648 19.226105386657 19.760915302727 19.762038815416 19.768539222306 19.769731627903 19.771364071808 19.775686400161 19.778416363799 19.779862292217 19.783919778107 19.791767848406 19.79467524218 19.807369571378 19.810440589782 19.820084152955 19.821879894848 19.829484376103 19.843196573599 19.852804941577 Stated Weight Actual Weight 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 19.854420930086 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 20kg 19.855412970489 19.868849940412 19.868850695769 19.874128258378 19.875213633228 19.876400272867 19.878895555655 19.880764903913 19.898388077135 19.899637159994 19.900248234856 19.902474494351 19.916631271256 19.91836667123 19.919563810606 19.925835845918 19.932603224688 19.937618826554 19.940483728491 19.952008158342 19.960191570696 19.966399052881 19.971487078761 19.975117310741 19.980704571086 19.981334692219 20.005450946738 20.009227204313 20.01261803118 20.015546045769 20.016178468223 20.022988209927 20.024705030489 20.025027340338 20.030841084733 20.04181135738 20.044428165377 20.044925661714 20.048921539018 20.048959778252 20.051933140019 20.062846928986 20.065757756548 20.070741735804 20.072247759964 20.078947731703 20.081382874002 20.085773412207 20.088741030918 20.09118645181 20.093233387125 20.102275047671 20.106831062998 20.123765395894 20.13030569307 20.130753490213 20.141885955943 20.14218383035 20.142755172783 20.148641619591 20.154639626492 20.163831293787 20.177500276537 20.184519232016 20.187377109666 20.188895705149 20.195997281323 20.203554190026 20.203985639679 20.210046885233 20.213167019793 20.215614294569 20.218406254291 20.219187358543 20.226215548629 20.227022282728 20.230176795325 21.075724526062 22.059187362402 Stated weight actual weight 20kg 17.404082900994 20kg 18.262151568893 20kg 17.396012400322 20kg 19.130773624794 20kg 19.231598141749 20kg 19.763183456686 20kg 19.764649690775 20kg 19.767694678039 20kg 19.769343458739 20kg 19.779045247658 20kg 19.791656125774 20kg 19.794417269807 20kg 19.795285715149 20kg 19.800621440863 20kg 19.801161703397 20kg 19.812920669061 20kg 19.81830019184 20kg 19.818596088735 20kg 19.825150073575 20kg 19.842386296258 20kg 19.842793147146 20kg 19.846012970075 20kg 19.857181247772 20kg 19.857549628304 20kg 19.860930514417 20kg 19.87433871758 20kg 19.879278937034 20kg 19.880163061105 20kg 19.884399529471 20kg 19.892496029115 20kg 19.893958886815 20kg 19.900930976037 20kg 19.904978483508 20kg 19.909965315239 20kg 19.916453716499 20kg 19.922159011391 20kg 19.924236015167 20kg 19.931181467392 20kg 19.932611766089 20kg 19.94312827711 20kg 19.955417695826 20kg 19.972572407899 20kg 19.973125145954 20kg 19.99134343415 20kg 19.997291206864 20kg 19.998345960438 20kg 20.003600248474 20kg 20.005912683873 20kg 20.009474557379 20kg 20.016841330227 20kg 20.017022457427 20kg 20.017706123226 20kg 20.018583549193 20kg 20.018694521649 20kg 20.019536627357 20kg 20.023855435906 20kg 20.034615564596 20kg 20.040521958364 20kg 20.041343960647 20kg 20.056751914604 20kg 20.058750718863 20kg 20.066673548005 20kg 20.067052187889 20kg 20.073760520267 20kg 20.085183390656 20kg 20.088371501066 20kg 20.095858755121 20kg 20.100269512457 20kg 20.104638543576 20kg 20.12307903952 20kg 20.124663798255 20kg 20.130243295275 20kg 20.139747676376 20kg 20.147677604248 20kg 20.158732053527 20kg 20.160363276699 20kg 20.16310017769 20kg 20.169468678004 20kg 20.171866311075 20k 20.175633789093 20kg 20.179858417394 20kg 20.182060105395 20kg 20.188086712093 20kg 20.190524057499 20kg 20.191450753385 20kg 20.205278653376 20kg 20.205291363676 20kg 20.207000831464 20kg 20.208905408291 20kg 20.21445462565 20kg 20.222234385737 20kg 20.2302877994 20kg 20.231835513941 20kg 20.237999799474 20kg 20.241179178538 20kg 20.251525726458 20kg 22.315150575791 20kg 21.461207260986 20kg 21.740637667652 20kg 22.253561561708