1. Bill has completed a 10-question multiple-choice test on which he answered 7 questions correctly. Each question had one correct answer to be chosen from five alternatives. Bill says that he answered the test by randomly guessing the answers without reading the questions or answers. Define the random variable x to be the number of correct answers on this test, and construct the probability distribution if the answers were obtained by random guessing.
What is the probability that Bill guessed 7 of the 10 answers correctly?
2. The mean lifetime of a certain tire is 30,000 miles and the standard deviation is 2500 miles.
If we assume nothing about the shape of the distribution, approximately what percentage of all such tires will last between 25,000 and 37,500 miles?
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