IMathAS-libretexts

Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean $\displaystyle \mu={50}$ grams and standard deviation $\displaystyle \sigma={2}$ grams.

If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?

There is no way to evaluate this likelihood, since the sample size (n = 4) is too small.
There is about a 16% chance of this occurring.
There is about a 5% chance of this occurring.
There is about a 2.5% chance of this occurring.
It is extremely unlikely for this to occur; the probability is very close to 0.

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