Question

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1000 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? 59,000 miles 58,250 miles 61,000 miles 61,750 miles

Answer 1

Answer: 61,750 miles

Step-by-step explanation:

Given : The p-value of the tires to outlast the warranty = 0.96

The probability that corresponds to 0.96 from a Normal distribution table is 1.75.

Mean : $\mu=60,000\text{ miles}$

Standard deviation : $\sigma=1000\text{ miles}$

The formula for z-score is given by  : -

$z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ 1.75=\dfrac{x-60000}{1000}\\\\\Rightarrow\ x-60000=1750\\\\\Rightarrow\ x=61750$

Hence, the tread life of tire should be 61,750 miles if they want 96% of the tires to outlast the warranty.