Compare the mean of two samplings following normal distribution












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The following is a problem for A-level test that I don't know how to solve.



The weight of a pig is normally distributed with mean 375 g and standard deviation 22 g. The weight of a rabbit is normally distributed with mean 425 g and standard deviation 25 g.



i) Five pigs and four rabbits are randomly chosen. Find the probability that the pigs weigh more than the rabbits.



ii) Find the probability that the average weight of a sample of 10 rabbits will exceed the average weight of a sample of 8 pigs by at least 39 g.



Can someone help me? Thanks a lot!






probability statistics normal-distribution sampling







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    0












    $begingroup$


    The following is a problem for A-level test that I don't know how to solve.



    The weight of a pig is normally distributed with mean 375 g and standard deviation 22 g. The weight of a rabbit is normally distributed with mean 425 g and standard deviation 25 g.



    i) Five pigs and four rabbits are randomly chosen. Find the probability that the pigs weigh more than the rabbits.



    ii) Find the probability that the average weight of a sample of 10 rabbits will exceed the average weight of a sample of 8 pigs by at least 39 g.



    Can someone help me? Thanks a lot!






    probability statistics normal-distribution sampling







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      The following is a problem for A-level test that I don't know how to solve.



      The weight of a pig is normally distributed with mean 375 g and standard deviation 22 g. The weight of a rabbit is normally distributed with mean 425 g and standard deviation 25 g.



      i) Five pigs and four rabbits are randomly chosen. Find the probability that the pigs weigh more than the rabbits.



      ii) Find the probability that the average weight of a sample of 10 rabbits will exceed the average weight of a sample of 8 pigs by at least 39 g.



      Can someone help me? Thanks a lot!






      probability statistics normal-distribution sampling







      share|cite|improve this question









      $endgroup$




      The following is a problem for A-level test that I don't know how to solve.



      The weight of a pig is normally distributed with mean 375 g and standard deviation 22 g. The weight of a rabbit is normally distributed with mean 425 g and standard deviation 25 g.



      i) Five pigs and four rabbits are randomly chosen. Find the probability that the pigs weigh more than the rabbits.



      ii) Find the probability that the average weight of a sample of 10 rabbits will exceed the average weight of a sample of 8 pigs by at least 39 g.



      Can someone help me? Thanks a lot!






      probability statistics normal-distribution sampling




      probability statistics normal-distribution sampling






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 18 '18 at 9:34









      mappingmapping

      1778




      1778






















          1 Answer
          1






          active

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          1












          $begingroup$

          Guide:



          i)



          Let $P_i$ be normally distributed for $i=1,2,3,4,5$ with the parameters that you mention for a pig.



          Let $R_i$ be normally distributed for $i=1,2,3,4$ with the parameters that you mention for a rabbit.



          Then $X:=P_1+P_2+P_3+P_4+P_5-R_1-R_2-R_3-R_4$ has normal distribution.



          Now find the parameters of this distribution and then find $P(X>0)$.



          ii)



          If $overline P$ denotes the average weight of $8$ pigs, and $overline R$ denotes the average weight of $10$ rabbits.



          Then $Y:=overline R-overline P$ has normal distribution.



          Now find the parameters of this distribution and then find $P(Y>39)$ or equivalently $P(Y-39>0)$.






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @p32fr4 Thank you, I overlooked the $39$.
            $endgroup$
            – drhab
            Dec 18 '18 at 10:07










          • $begingroup$
            Understood! Thanks a lot!
            $endgroup$
            – mapping
            Dec 18 '18 at 11:22










          • $begingroup$
            You are welcome.
            $endgroup$
            – drhab
            Dec 18 '18 at 11:23











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          1 Answer
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          1 Answer
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          active

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          active

          oldest

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          active

          oldest

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          1












          $begingroup$

          Guide:



          i)



          Let $P_i$ be normally distributed for $i=1,2,3,4,5$ with the parameters that you mention for a pig.



          Let $R_i$ be normally distributed for $i=1,2,3,4$ with the parameters that you mention for a rabbit.



          Then $X:=P_1+P_2+P_3+P_4+P_5-R_1-R_2-R_3-R_4$ has normal distribution.



          Now find the parameters of this distribution and then find $P(X>0)$.



          ii)



          If $overline P$ denotes the average weight of $8$ pigs, and $overline R$ denotes the average weight of $10$ rabbits.



          Then $Y:=overline R-overline P$ has normal distribution.



          Now find the parameters of this distribution and then find $P(Y>39)$ or equivalently $P(Y-39>0)$.






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @p32fr4 Thank you, I overlooked the $39$.
            $endgroup$
            – drhab
            Dec 18 '18 at 10:07










          • $begingroup$
            Understood! Thanks a lot!
            $endgroup$
            – mapping
            Dec 18 '18 at 11:22










          • $begingroup$
            You are welcome.
            $endgroup$
            – drhab
            Dec 18 '18 at 11:23
















          1












          $begingroup$

          Guide:



          i)



          Let $P_i$ be normally distributed for $i=1,2,3,4,5$ with the parameters that you mention for a pig.



          Let $R_i$ be normally distributed for $i=1,2,3,4$ with the parameters that you mention for a rabbit.



          Then $X:=P_1+P_2+P_3+P_4+P_5-R_1-R_2-R_3-R_4$ has normal distribution.



          Now find the parameters of this distribution and then find $P(X>0)$.



          ii)



          If $overline P$ denotes the average weight of $8$ pigs, and $overline R$ denotes the average weight of $10$ rabbits.



          Then $Y:=overline R-overline P$ has normal distribution.



          Now find the parameters of this distribution and then find $P(Y>39)$ or equivalently $P(Y-39>0)$.






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @p32fr4 Thank you, I overlooked the $39$.
            $endgroup$
            – drhab
            Dec 18 '18 at 10:07










          • $begingroup$
            Understood! Thanks a lot!
            $endgroup$
            – mapping
            Dec 18 '18 at 11:22










          • $begingroup$
            You are welcome.
            $endgroup$
            – drhab
            Dec 18 '18 at 11:23














          1












          1








          1





          $begingroup$

          Guide:



          i)



          Let $P_i$ be normally distributed for $i=1,2,3,4,5$ with the parameters that you mention for a pig.



          Let $R_i$ be normally distributed for $i=1,2,3,4$ with the parameters that you mention for a rabbit.



          Then $X:=P_1+P_2+P_3+P_4+P_5-R_1-R_2-R_3-R_4$ has normal distribution.



          Now find the parameters of this distribution and then find $P(X>0)$.



          ii)



          If $overline P$ denotes the average weight of $8$ pigs, and $overline R$ denotes the average weight of $10$ rabbits.



          Then $Y:=overline R-overline P$ has normal distribution.



          Now find the parameters of this distribution and then find $P(Y>39)$ or equivalently $P(Y-39>0)$.






          share|cite|improve this answer











          $endgroup$



          Guide:



          i)



          Let $P_i$ be normally distributed for $i=1,2,3,4,5$ with the parameters that you mention for a pig.



          Let $R_i$ be normally distributed for $i=1,2,3,4$ with the parameters that you mention for a rabbit.



          Then $X:=P_1+P_2+P_3+P_4+P_5-R_1-R_2-R_3-R_4$ has normal distribution.



          Now find the parameters of this distribution and then find $P(X>0)$.



          ii)



          If $overline P$ denotes the average weight of $8$ pigs, and $overline R$ denotes the average weight of $10$ rabbits.



          Then $Y:=overline R-overline P$ has normal distribution.



          Now find the parameters of this distribution and then find $P(Y>39)$ or equivalently $P(Y-39>0)$.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 18 '18 at 10:05









          p32fr4

          3717




          3717










          answered Dec 18 '18 at 9:53









          drhabdrhab

          101k545136




          101k545136








          • 1




            $begingroup$
            @p32fr4 Thank you, I overlooked the $39$.
            $endgroup$
            – drhab
            Dec 18 '18 at 10:07










          • $begingroup$
            Understood! Thanks a lot!
            $endgroup$
            – mapping
            Dec 18 '18 at 11:22










          • $begingroup$
            You are welcome.
            $endgroup$
            – drhab
            Dec 18 '18 at 11:23














          • 1




            $begingroup$
            @p32fr4 Thank you, I overlooked the $39$.
            $endgroup$
            – drhab
            Dec 18 '18 at 10:07










          • $begingroup$
            Understood! Thanks a lot!
            $endgroup$
            – mapping
            Dec 18 '18 at 11:22










          • $begingroup$
            You are welcome.
            $endgroup$
            – drhab
            Dec 18 '18 at 11:23








          1




          1




          $begingroup$
          @p32fr4 Thank you, I overlooked the $39$.
          $endgroup$
          – drhab
          Dec 18 '18 at 10:07




          $begingroup$
          @p32fr4 Thank you, I overlooked the $39$.
          $endgroup$
          – drhab
          Dec 18 '18 at 10:07












          $begingroup$
          Understood! Thanks a lot!
          $endgroup$
          – mapping
          Dec 18 '18 at 11:22




          $begingroup$
          Understood! Thanks a lot!
          $endgroup$
          – mapping
          Dec 18 '18 at 11:22












          $begingroup$
          You are welcome.
          $endgroup$
          – drhab
          Dec 18 '18 at 11:23




          $begingroup$
          You are welcome.
          $endgroup$
          – drhab
          Dec 18 '18 at 11:23


















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