Answer:
(a) The integral in total indicates the probability of a randomly selected tire having a lifetime between 40,000 miles to 50,000 miles.
(b) The integral in total indicates the probability of a randomly selected tire having a lifetime of at least 25,000 miles.
Step-by-step explanation:
The probability density function for the lifetime of a manufacturer's highest quality car tire is denoted by, f (x).
(a)
The integral given is:
[tex]\int\limits^{50,000}_{40,000} {f(x)}\, dx[/tex]
The values 40,000 and 50,000 indicates the limits of the integral.
It implies that the integral is to be solved over the range (40,000 - 50,000) miles.
And the integral in total indicates the probability of a randomly selected tire having a lifetime between 40,000 miles to 50,000 miles.
(b)
The integral given is:
[tex]\int\limits^{\infty}_{25,000} {f(x)}\, dx[/tex]
The values 25,000 and ∞ indicates the limits of the integral.
It implies that the integral is to be solved over the range (25,000 - ∞) miles.
And the integral in total indicates the probability of a randomly selected tire having a lifetime of at least 25,000 miles.
