Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 grams.
If the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised?
1. There is no way to evaluate this likelihood, since the sample size (n = 9) is too small.
2. It is extremely unlikely for this to occur; the probability is very close to 0.
3. There is about a 5% chance of this occurring.
4. There is about a 16% chance of this occurring.
5. There is about a 2.5% chance of this occurring.
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