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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Nia

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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Colton Ballard · Answer 1

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