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Have I done the sample proportion method correctly for this central limit theorem problem ?
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https://preview.redd.it/8jyn4gw3kjtc1.png?width=1822&format=png&auto=webp&s=1e8131c57e1e5bea4d82dd28a2db2f668b188a56

my prof says we should always try to cmpare our answers both in probability and with that of a sample proporiton,

I know its silly but can someone please check my work on this problem here:

https://preview.redd.it/5da31mu9kjtc1.png?width=2572&format=png&auto=webp&s=799224281db3b6a93e560661a1077bc2f35bbe98

here is my work but idk why I do NOT feel confident about this:

https://preview.redd.it/tdptvohfkjtc1.png?width=1786&format=png&auto=webp&s=28014500868dedc5140b4617fbea4f2254dedbdd

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7 months ago