Government regulations indicate that the total weight of cargo in a certain kind of airplane cannot exceed 330 kg. On a particular day a plane is loaded with 100 boxes of goods. If the weight distribution for individual boxes is normal with mean 3.2 kg and standard deviation 0.7 kg, what is the probability that the regulations will NOT be met (round to the nearest integer).

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Government regulations indicate that the total weight of cargo in a certain kind of airplane cannot exceed 330 kg. On a particular day a plane is loaded with 100 boxes of goods. If the weight distribution for individual boxes is normal with mean 3.2 kg and standard deviation 0.7 kg, what is the probability that the regulations will NOT be met (round to the nearest integer).

Mathematics
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I think theres some kind of formula associated with standard deviation
\(\mu = 3.2\) \(\sigma=0.7\)

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By central limit theorem, the sample parameters will be : \(\overline{x}=3.2\) \(s=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.7}{\sqrt{100}}=0.07\) use them to find \(P(\overline{x}\le 3.3)\)

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