Question

A tire company produces tires for​ mid-sized sedans. The tires are guaranteed to last for 30 comma 000 ​miles, but some will fail sooner and some will last many more miles beyond 30 comma 000. The lifetime in miles of a tire is described by a continuous random variable L. Let f be the probability density function for the random variable L. Explain the meaning of the integrals in parts ​(a) through ​(d). a. What is the meaning of the integral Integral from 26 comma 000 to 33 comma 000 f (Upper L )dL​?

Answer 1

Answer:

The integral is the probability that the tire will fail in at some point between 26000 and 32000 miles.

Step-by-step explanation:

Consider the provided integral.

$\int\limits^{32,000}_{25,000} F({L}) \, dL$

It is given that the tires are guaranteed to last for 30,000 ​miles, but some will fail sooner and some will last many more miles beyond 30,000.

And f(L) be the probability density function for the random variable L.

According to the probability density function (PDF):

The PDF is used to determine the likelihood of a random variable falling within a specified range of values.

Thus, the integral:  

$\int\limits^{32,000}_{25,000} F({L}) \, dL$

Gives us the integral is the probability that the tire will fail in at some point between 26000 and 32000 miles.