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I am learning A-Level Statistics together with my child and came across this problem:

enter image description here

I then double-checked with ChatGPT, and it gave this answer:

enter image description here

So who is right? Should we use Var(S) = $3^2$Var(S) as stated in the textbook, or Var(S) = 3*Var(S) as recommended by ChatGPT?

Math_Physics
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    Which A-level textbook is this? I actually think this is wrong as well. – daruma Apr 29 '23 at 01:59
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    The $3^2S+T$ formula suggests that the distribution of bars of soap are not independently distributed. That is that the person filling the package will choose the first bar at random, and then find 2 more matching bars. Or, there is a machine that cuts bars of soap that could spit out large bars one day and small bars the next, but all bars that it produces in a batch will be the same size. – user317176 Apr 29 '23 at 02:13
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    We are not here to debug ChatGPT. – JonathanZ Apr 29 '23 at 02:28
  • Dear daruma, the ISBN is 9781108407342. – Math_Physics Apr 29 '23 at 03:03
  • ChatGPT is not a computer algebra system. It does not "understand" mathematics, and is not designed to understand mathematics. It is not a useful tool for doing mathematical tasks. Questions about GPT output are not on-topic here. – Xander Henderson Apr 29 '23 at 19:51

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You're getting 3 different bars of soap, so it should be $S_1,S_2,S_3$ all identically distributed. So in this case, ChatGPT is correct.

Not $3S$, because you're not getting one bar of soap and cloning it three times. Where did you get the textbook?

Benjamin Wang
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    Please do not create answers for low quality questions. – JonathanZ Apr 29 '23 at 02:34
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    Dear Benjamin, thank you for the explanation. The ISBN is 9781108407342. I like the author's math books: there are very few errata, unlike other textbooks that I have read. – Math_Physics Apr 29 '23 at 03:07
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    I am trying to help my kid on his study. We came across a problem, I have doubts about the calculation given in the textbook, I ask ChatGPT for advice (we are self-studying at home), and try to find more insights how the variance is calculated on various situations.

    I painstakingly spent time piecing the questions/images together, hoping that it is clear to somebody like Benjamin Wang who may be kind enough to show some lights to math beginner like me.

    Please show some passions to others who try to learn. If the question is of low quality, please be more constructive and suggest.

     – Math_Physics Apr 29 '23 at 03:44
  • Do not let look ChatGPT to be a useful tool. – Peter May 02 '23 at 13:15