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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 Binomial, Standard Deviation, Household income in the United States, $200

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