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Math Help - normal probability distribution

  1. #1
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    normal probability distribution

    The Dynamic Tire Co. has just developed a new steel-belted radial tire to be sold through a national chain of discount stores. From road tests, it is found the tire life is normally distributed with a mean life of 73,000km and a standard deviation of 6,000km.

    Dynamic plans to give a guarantee on their tires, under which they will replace any tire that wears out prematurely. What should their guarantee be, if they only wish to replace at most 1.5% of all tires?

    The answer is 0.59980 but I want to know how you get this answer because I don't know how they got it.

    Thank you!
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  2. #2
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    Quote Originally Posted by shellshock View Post
    The Dynamic Tire Co. has just developed a new steel-belted radial tire to be sold through a national chain of discount stores. From road tests, it is found the tire life is normally distributed with a mean life of 73,000km and a standard deviation of 6,000km.

    Dynamic plans to give a guarantee on their tires, under which they will replace any tire that wears out prematurely. What should their guarantee be, if they only wish to replace at most 1.5% of all tires?

    The answer is 0.59980 but I want to know how you get this answer because I don't know how they got it.

    Thank you!
    Find the value z* such that Pr(Z > z*) > 0.015. Then the value of x* such that Pr(X > x*) = 0.015 is found by solving z^* = \frac{x^* - 73,000}{6,000} for x*.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Find the value z* such that Pr(Z > z*) > 0.015. Then the value of x* such that Pr(X > x*) = 0.015 is found by solving z^* = \frac{x^* - 73,000}{6,000} for x*.
    thanks!
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