1) What is meant, if data follow a bell curve or normal distribution? What are some examples of quantities that are typically normally distributed?
2) What proportion of the data in a normal distribution lies within one standard deviation of the mean? Within two standard deviations? Three?
1) Automated machinery is used to fill boxes of Chocolate Frosted Sugar Bombs breakfast cereal. The machine is calibrated to put an average of 16.4 ounces of cereal in each box. Minor variation in the process causes the standard deviation to be 0.2 ounces.
a) What percentage of the boxes of cereal weigh less than 16 ounces?
b) What percentage weigh between 16.2 and 16.8 ounces?
c) What percentage are more than 17.4 ounces?
2) A recent anthropological study of the aboriginal dwarf pygmies living on the island of Kafoonistan has shown that adult males in the tribe have an average height of 60″, with a standard deviation of 4″.
a) What percentage of the men of the tribe are over six feet (72″) tall?
b) How tall are the tallest 10% of the men in the tribe?
c) How short are the shortest 20% of the men in the tribe?
3) Daily stock market returns on the Boravian Stock Exchange are approximately normally distributed, with a mean of 0.05% and a standard deviation of 0.5%.
a) What percentage of the time are daily returns positive (i.e., greater than 0%)?
b) What percentage of the time do daily returns drop by 2% or more?
1a) .0228 1b) .8185 1c) approx. 0
2a) .0013 2b) 65.12″ or more 2c) 56.64″ or less
3a) .5398 3b) approx. 0
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