The British chocolate manufacturer Cadbury in Birmingham is wel a wide range of products, from chocolate bars, cakes, desserts to biscuits. In this manufacturer, a machine is programmed to distribute 1600 grams of chocolate bars into every box. However, some boxes include slightly less chocolate bars than 1600 grams and some have significantly more. With a mean of 1600 grams and a standard deviation of 18 grams, the total amount of chocolate bar in all the boxes exhibits a normal distribution. (a) Calculate the probability that a randomly selected box contains 1620 to 1650 grams of chocolate bar. (b) (c) Examine the percentage of such boxes contain less than 1570 grams of choco- late bar. Give an explanation on the possibility for a box less than 1520 grams of choco- late bar.

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