Balls are placed into boxes containing 100. After inspection of a large numbers of boxes the average number of deflated balls was found to be 10 with a standard deviation of 3. Assuming that the same conditions continue, except that boxes containing 300 were used, What would be the average number and standard deviation of deflated balls per box and how many balls must each box hold so that the standard deviation of the number of deflated balls is equal to 1% of the total number of balls in the box?
2026-04-01 01:36:40.1775007400
Calculate mean and standard deviation of new sample based on old
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The question is vague, but it seems clear that in a box of 100 balls, there will be 10±3 deflated balls. Scaling this up by a factor of 3, you have a mean of 30 deflated balls with a standard deviation of 9.
Taking into consideration that the symbol for variance is σ^2, and if I am correct that the standard deviation of the new sample is 9, I would assume the variance of the new sample to be 9^2 = 81.