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#1 2006-07-09 12:28:15

babyangel1972
Member
Registered: 2005-12-12
Posts: 18

Help

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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#2 2006-07-09 16:51:59

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Help

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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