I've tried to use similar questions for this, but I ended up with just a horrible answer. I have a question about a woman serving soup, she originally had 30 litres for 80 pupils, with expectation 0.25 litres and variance 0.005 litres^2, no pdf or distribution is given, but the amounts are independent across pupils.

The question I'm stuck on says: 'after all 80 pupils have been served, Cathy has used up just 19 litres of soup. She wonders if she can give all pupils a second helping. The variance of the amount she serves each pupil is fixed, but she can alter its expectation. Use Chebyshev's inequality to derive for her the maximum expected amount of second helping soup per pupil that ensures the probability the pupils all receive a second helping is at least 0.6'

The way I tried I got an expectation of around 7. But this is clearly wrong...


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