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8 March, 13:42

A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 48,400 miles and a standard deviation of 5000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?

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  1. 8 March, 15:30
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    Approximate number of miles for a warranty = 41,990

    Explanation:

    Given:

    Mean distribution = 48,400 miles

    Standard deviation = 5,000 miles

    Z score table less then 10% = 1.282 (according to t table)

    Approximate number of miles for a warranty = ?

    Computation of approximate number of miles for a warranty:

    Approximate number of miles for a warranty = Mean distribution + (Standard deviation = 5,000) (-Z score table less then 10%)

    Approximate number of miles for a warranty = 48,400 + (5,000) (-1.282)

    Approximate number of miles for a warranty = 48,400 - 6,410

    Approximate number of miles for a warranty = 41,990
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