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In: Statistics and Probability

A tire manufacturer warranties its tires to last at least 20 comma 000 miles or​ "you...

A tire manufacturer warranties its tires to last at least 20 comma 000 miles or​ "you get a new set of​ tires." In its​ experience, a set of these tires last on average 28 comma 000 miles with SD 5 comma 000 miles. Assume that the wear is normally distributed. The manufacturer profits ​$200 on each set​ sold, and replacing a set costs the manufacturer ​$400. Complete parts a through c.

​(a) What is the probability that a set of tires wears out before 20 comma 000 ​miles? The probability is nothing that a set of tires wears out before 20 comma 000 miles. ​(Round to four decimal places as​ needed.)

​(b) What is the probability that the manufacturer turns a profit on selling a set to one​ customer? The probability is nothing that the manufacturer turns a profit on selling a set to one customer. ​(Round to four decimal places as​ needed.)

​(c) If the manufacturer sells 500 sets of​ tires, what is the probability that it earns a profit after paying for any​ replacements? Assume that the purchases are made around the country and that the drivers experience independent amounts of wear. The probability is nothing that the manufacturer earns a profit after paying for any replacements on 500 sets of tires. ​(Round to four decimal places as​ needed.)

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