Answer: 0.9726
Step-by-step explanation:
Let x be the random variable that represents the distance the tires can run until they wear out.
Given : The top-selling Red and Voss tire is rated 50,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a [tex]\mu=[/tex]67,000 miles and a [tex]\sigma=[/tex] 5,200 miles.
Then , the probability that a tire wears out before 60,000 miles :
[tex]P(x<60000)=P(\dfrac{x-\mu}{\sigma}<\dfrac{60000-50000}{5200})\\\\=P(z<1.92)=0.9726[/tex] [using p-value table for z]
Hence, the probability that a tire wears out before 60,000 miles= 0.9726
