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Binomial, Poission

# Binomial, Poission - 1[2007 AJC JC2 MYE Q13 Butter is sold...

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1. [2007 AJC JC2 MYE Q13] Butter is sold in blocks of two different sizes: large and small. The weight of a randomly chosen small block is normally distributed with mean 253g and standard deviation 4g. The weight of a randomly chosen large block is normally distributed with mean 505g and standard deviation 6g. The weight of any block of butter may be assumed to be independent of the weight of any other block. (i) Find the probability that a randomly chosen small block of butter weighs less than 248g. (ii) If 4 small blocks of butter are chosen, find the probability that two of them weigh less than 248g, one of them weighs more than 253g and the remaining one weighs between 248g and 253g. (iii)Find the probability that the total weight of 2 large blocks is more than 4 times the weight of a small block b at least 5 g. (iv)Due to a change in the packaging process, the mean weight of a randomly chosen large block of butter is changed to μ g. If the standard deviation is

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