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A tire company tested a particular model of super radial tire and found the tires to be normally distributed with respect to wear. The "average" (mean) tire wore out at 59,000 miles , and the standard deviation was 2500 miles.
a. If 2000 tires are tested, about how many are likely to wear out before 54,000 miles?
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Using basic statistics, we realize that we need to write out the formula for the Guassian distribution:
Then to find the probability that the tire will wear out before 54,000 miles, we simply integrate:
Then out of 2,000 tires,
are likely to wear out before 54,000 miles. Note that a 46th tire begins to wear out halfway but doesn't completely make the transformation to a worthless tire.
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