# Sampling Distributions, Probability

Sampling Distributions, Probability 150 150 Affordable Capstone Projects Written from Scratch

Sampling Distributions

Show all workings.

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:

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

(3 marks)

• Suppose now you purchase a pack of 4 bars and measure their mean weight.
• Describe the probability distribution of the mean weight.
• What is the probability that the mean weight of the pack of 4 is under weight?

(5 marks)

• Explain in your own words why the probability in (b)(ii) is much smaller than that in (a).

(2 marks)

You must draw graphs for parts (a) and (b) and show all workings. Answers without correct graphs and workings will not score full marks.

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