2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating that the maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult male passengers, since they tend to be heavier than women or children. Assume adult male weights are normally distributed with a mean of 188.6 Ib. and standard deviation of 38.9 Ib. a.) If 12 men weighed exactly 2004 lb., what would be the average weight? b.) Find the probability that a single man will have a weight greater than your result from part (a). c.) Find the probability that 12 randomly selected men will have a weight greater than your results from part (a). d.) Does the gondola appear to have the correct weight limit? Why or why not?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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