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A tire company finds that the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3,000 miles. If the manufacturer does not want to replace more than 5% of the tires, what should be the approximate number of miles for the warranty? • Use a TI-83, TI-83 plus, or TI-84 calculator, and round your answer to the nearest Integer

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Answer:

42580 miles

Step-by-step explanation:

Mean = [tex]\mu = 47500[/tex]

[tex]\sigma = 3000[/tex]

The manufacturer does not want to replace more than 5% of the tires

[tex]P(X\leq x)=5\%[/tex]

[tex]P(\frac{x-\mu}{\sigma}\leq \frac{x-47500}{3000})=0.05[/tex]

By using normal table values :

[tex]\frac{x-47500}{3000}=-1.64[/tex]

[tex]x=(-1.64 \times 3000)+47500[/tex]

[tex]x=42580[/tex]

Hence the approximate number of miles for the warranty is 42580 miles

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