(b) Suppose that 115 packs of potato chips are randomly chosen. Find the probability that at most 57 packs of potato chips weigh at least 79.91 g.

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I would like to ask Qb. I think it's using the normal approximation to calculate the answer but I can't.

2. It is known that weights of packs of potato chips produced by a certain factory
follow a normal distribution of mean 80 g and standard deviation 0.8 g.
(a) Suppose that 115 packs of potato chips are randomly chosen. Find the probability
that their average weight is at least 79.91 g.
(b) Suppose that 115 packs of potato chips are randomly chosen. Find the probability
that at most 57 packs of potato chips weigh at least 79.91 g.
(c) Suppose that 22 packs of potato chips are randomly chosen and let s 2 be the
sample variance of their weights. Find positive numbers K1 and K2 so that P(s > K2) =
P(s < K1) and P(K1 < s < K2) = 0.8.
Transcribed Image Text:2. It is known that weights of packs of potato chips produced by a certain factory follow a normal distribution of mean 80 g and standard deviation 0.8 g. (a) Suppose that 115 packs of potato chips are randomly chosen. Find the probability that their average weight is at least 79.91 g. (b) Suppose that 115 packs of potato chips are randomly chosen. Find the probability that at most 57 packs of potato chips weigh at least 79.91 g. (c) Suppose that 22 packs of potato chips are randomly chosen and let s 2 be the sample variance of their weights. Find positive numbers K1 and K2 so that P(s > K2) = P(s < K1) and P(K1 < s < K2) = 0.8.
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