Suppose that a candy company makes a candy bar whose weight is supposed to be 50

Question

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 mu = 50 grams and standard deviation 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.

Explanation / Answer

here for normal distribution , z=(X-mean)/std error

std error for mean =std deviation/(n)1/2 =2/(4)1/2 =1

hence probabilty that average weight is 4 or more gram less=P(X<46)=P(Z<(46-50)/1)=P(Z<-4)=0.0000

hence it is extremely unlikely for this to occur, the probability is very close to 0/

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