Question

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

Answer 1

Answer:

42580 miles

Step-by-step explanation:

Mean = $\mu = 47500$

$\sigma = 3000$

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

$P(X\leq x)=5\%$

$P(\frac{x-\mu}{\sigma}\leq \frac{x-47500}{3000})=0.05$

By using normal table values :

$\frac{x-47500}{3000}=-1.64$

$x=(-1.64 \times 3000)+47500$

$x=42580$

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