A pack of potato chips is randomly chosen from the outputs of machine A. Find the probability that it weighs less than 79.9 g. (b) A pack of potato chips is randomly chosen from the outputs of machine B. Find the probability that it weighs less than 79.9 g. (c) A pack of potato chips is randomly chosen from the outputs of this factory and is found to weigh less than 79.9 g. Find the probability that it was produced by machine A
A factory is producing packs of potato chips using two machines, A and B, only. It is known that the weights of the packs of potato chips produced by machine A follow a normal distribution of mean 79.8 g and standard deviation 0.6 g, while the weights of the packs of potato chips produced by machine B follow a normal distribution of mean 80.1 g and standard deviation 0.5 g. It is known that about 42% of the packs of potato chips produced by this factory weigh less than 79.9 g.
(a) A pack of potato chips is randomly chosen from the outputs of machine A. Find the probability that it weighs less than 79.9 g.
(b) A pack of potato chips is randomly chosen from the outputs of machine B. Find the probability that it weighs less than 79.9 g.
(c) A pack of potato chips is randomly chosen from the outputs of this factory and is found to weigh less than 79.9 g. Find the probability that it was produced by machine A.
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