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?

Question

Bright

Business

18 February, 00:05

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?

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Abraham · Answer 1

2.5%

Explanation:

Probability of such occurring = P (x≤28) because from the scenario it states that each bag weighs 30 grams but we seek a probability that a bag is 2 or more grams less than 30 (which means its is equal or less than 28).

Given that this is a normal distribution with mean μ = 30 grams and standard deviation σ = 3 grams. implies that standard deviation = 3 / √ 9 = 1

Hence P (x≤28) = P (z≤2) = 0.025 or 2.5%