*Use the dataset provided below for this problem. You will get a list of weights for 20kg weight plates made by two companies (A) and (B).

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 A versus Company B. 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 A weights:

Slated weigm actual weighl 20kg 17404082900994 20kg 13262151563893 20kg 1 7.39601 2400322 20kg 19.130773624794 20kg 19.231593141749 20kg 19763183456686 20kg 1 9764649690775 20kg 1 9767694673039 20kg 1 9769343453739 20kg 1 9779045247653 20kg 19791655125774 20kg 19.794417269807 20kg 19.795285715149 20kg 19800621440863 20kg 19.801161703397 20kg 19812920669061 20kg 1981330019184 20kg 1981I595083735 20kg 19825150073575 20kg 1 9842385295253 20kg 19842793147146 20kg 1 9.84601 2970075 20kg 19.857181247772 20kg 19.857549623304 20kg 19860930514417 20kg 19.87433371758 20kg 1 9879273937034 20kg 19880163061105 20kg 1 9884399529471 20kg 19892495029115 20kg 19893953886815 20kg 1 9.900930976037 20kg 1 9904973483503 20kg 19909965315239 20kg 19915453715499 20kg 19922159011391 20kg 19924235015167 20kg 19931181467392 20kg 1993261 1765089 20kg 1994312927711 20kg 1 9.95541 7695826 20kg 1 9972572407899 20kg 19973125145954 20kg 1999134343415 20kg 19997291205864 20kg 1999345960433 20kg 20003600243474 20kg 20005912683873 20kg 20.009474557379 20kg 20.016841330227 20kg 20.017022457427 20kg 20.017706123226 20kg 20013583549193 20kg 20013694521649 20kg 20019535627357 20kg 20023855435905 20kg 2003461 5564595 20kg 20.040521953364 20kg 20041343960647 20kg 20.056751914604 20kg 2005975071 3863 20kg 20066673543005 20kg 20067052187889 20kg 20073760520267 20kg 20085183390655 20kg 20083371501065 20kg 20095853755121 20kg 20100269512457 20kg 20104633543576 20kg 2012307903952 20kg 20124663793255 20kg 20130243295275 20kg 20139747675375 20kg 20147677604243 20kg 20153732053527 20kg 20160363275699 20kg 2016310017769 20kg 20.169463673004 20kg 20.171866311075 20kg 20175633789093 20kg 20179853417394 20kg 20182060105395 20kg 2018I085712093 20kg 20190524057499 20kg 20191450753385 20kg 20205273653376 20kg 20205291363676 20kg 20207000831464 20kg 20209905403291 20kg 2021445462565 20kg 20222234385737 20kg 202302877994 20kg 20231835513941 20kg 20237999799474 20kg 20241179173533 20kg 20251525726453 20kg 22.315150575791 20kg 21461207260986 20kg 21 740637667652 20kg 22253561561703 Slated Weighl Actual Weight 20kg 1 7.78081 9976648 20kg 19226105386657 20kg 1 9.76091 5302727 20kg 1 9.76203881 541 6 20kg 1 9.768539222306 20kg 1 9769731627903 20kg 19771364071808 20kg 19775686400161 20kg 1 977841 6363799 20kg 1 9.77986229221 7 20kg 1 9.78391 9778107 20kg 19.791767848406 20kg 1 9.79467524218 20kg 1 9.807369571 378 20kg 19.81 0440589782 20kg 19820084152955 20kg 1 9821879894848 20kg 1 9829484376103 20kg 1 98431 96573599 20kg 1 9.852804941 577 20kg 1 9.854420930086 20kg 1 9.85541 2970489 20kg 1 9.86884994041 2 20kg 1 9.868850695769 20kg 1 98741 28258378 20kg 1 987521 3633228 20kg 1 9876400272867 20kg 1 9878895555655 20kg 1 9.88076490391 3 20kg 1 9898388077135 20kg 19.899637159994 20kg 1 9.900248234856 20kg 1 9 .902474494351 20kg 1991 6631271256 20kg 1991836667123 20kg 1991 9563810606 20kg 1 992583584591 20kg 1 9.932603224688 20kg 1 9.93761 8826554 20kg 1 9 .940483728491 20kg 19.952008158342 20kg 19960191570696 20kg 1 9 .966399052881 20kg 1 9971487078761 20kg 199751 17310741 20kg 1 9980704571 086 20kg 19981334692219 20kg 20005450946738 20kg 20 .00922720431 3 20kg 2001261803118 20kg 20 .01 5546045769 20kg 20 .01 6178468223 20kg 20022988209927 20kg 20024705030489 20kg 20025027340338 20kg 20030841084733 20kg 2004181135738 20kg 200444281 65377 20kg 20 .044925661 714 20kg 20 .048921 53901 8 20kg 20 .048959778252 20kg 20051933140019 20kg 20062846928986 20kg 20065757756548 20kg 20070741735804 20kg 20072247759964 20kg 20078947731 703 20kg 20 .081 382874002 20kg 20 .08577341 2207 20kg 20 .088741 03091 8 20kg 2009118645181 20kg 20 0932333871 25 20kg 20 '1 02275047671 20kg 29106831062998 20kg 20 .1 23765395894 20kg 20 .1 3030569307 20kg 20.13075349021 3 20kg 20.141885955943 20kg 20.14218383035 20kg 20.142755172783 20kg 20148641619591 20kg 20 '1 54639626492 20kg 29163831293787 20kg 20 .1 77500276537 20kg 20.184519232016 20kg 20.187377109666 20kg 20 .1 888957051 49 20kg 20.195997281 323 20kg 20 .2035541 90026 20kg 20 3203985639679 20kg 20 '21 0046885233 20kg 20 '21 3167019793 20kg 20 '21 5614294569 20kg 20 .21 8406254291 20kg 20.21 9187358543 20kg 20.22621 5548629 20kg 20 .227022282728 20kg 20.2301 76795325 20kg 21 075724526062 20kg 22 30591 87362402