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?
(c) Explain why the probability in (b)(ii) is much smaller than that in (a).
Draw graphs for parts (a) and (b) and show all workings.