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Question from 2019 Probability paper

Hello!

I have a question about the 2019 Probability L2 question d(ii)

So based on the answer in question d(i), there is a 0.05% chance that two randomly selected plates made by Eddy would weigh over 520g. So in my answer I mentioned that his mean is probably higher than the companies.

But in terms of standard deviation, the marking schedule says that Eddy’s standard deviation is also higher than the company’s. I can see why because greater standard deviation means greater spread, therefore more chance of choosing plates that are of greater weight.
However, in my answer, I said that standard deviation could be lower because the fact that Eddy randomly chooses plates that both weighed over 520g shows that his data is somewhat consistent, which means less variation, therefore, a smaller standard deviation. Is this thinking correct?

Thanks

Welcome @11111111

Thanks for your question. Because the odds of him picking two plates at random and them both being over 520g is very small it is indicating that his own distribution may be different. By chance alone is is highly unlikely that the two plates would be more than 520g. This means that his distribution could be shifted further up the scale i.e. a higher mean. Alternatively he may have more variation in the weights of plates that he produces therefore his distribution having a bigger SD.

I can see what you are trying to say with having both a higher mean and a smaller SD. This would only work if the mean quite close to 520g for this very tight distribution to work. Also a sample of 2 plates is not really enough to say that his plates are consistently over 520g. We just want to alter the distribution to make this more likely than it currently is.

It would be safer to give the answer that his distribution is more spread out than the regular one or that his mean is higher. The plates are meant to have a mean of 450g for this company.

I hope this clarifies things.

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