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Let f ( x ) be the probability density function for the lifetime of a manufactur

ID: 2859963 • Letter: L

Question

Let

f(x)

be the probability density function for the lifetime of a manufacturer's highest quality car tire, where x is measured in miles. Explain the meaning of each integral.

(a)    

The integral is the probability that a randomly chosen tire will have a lifetime of exactly 50,000 miles.

The integral is the probability that a randomly chosen tire will have a lifetime under 50,000 miles.

The integral is the probability that a randomly chosen tire will have a lifetime between 40,000 and 50,000 miles.

The integral is the probability that a randomly chosen tire will have a lifetime of at least 40,000 miles.


(b)    

The integral is the probability that a randomly chosen tire will have a lifetime of at least 25,000 miles.

The integral is the probability that a randomly chosen tire will have a lifetime of exactly 25,000 miles.    

The integral is the probability that a randomly chosen tire will not wear out.

The integral is the probability that a randomly chosen tire will have a lifetime under 25,000 miles.

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Explanation / Answer

(a) The integral is the probability that a randomly chosen tire will have a lifetime between 40,000 and 50,000 miles.

(b) The integral is the probability that a randomly chosen tire will have a lifetime of at least 25,000 miles.