(Answered) Manufacturer of lindts chocolate bar claims that the net

Statistics

Manufacturer of Lindt's Chocolate bar claims that the net weight of its 150g Hazelnut Chocolate bar is normally distributed with a mean of 155 g and a standard deviation of 3g.

Assuming that the claim is correct, answer the following questions:

(a) If you purchase one 150g Hazelnut Chocolate bar, what is the probability that its net weight is under weight (i.e. less than 150g)?

(b) Suppose now you purchase a pack of 4 bars and measure their mean weight.

(i) Describe the probability distribution of the mean weight.

(ii) What is the probability that the mean weight of the pack of 4 is under weight?

Draw graphs for parts (a) and (b) and show all workings.

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