Problem 71E

Average lifetime The average time until a computer chip fails (see Exercise 70) is . Find this value.

Exercise 70

Electronic chips Suppose the probability that a particular computer chip fails after t = a hours of operation is .

a. Find the probability that the computer chip fails after 15,000 hr of operation.

b. Of the chips that are still operating after 15,000 hr. what fraction of these will operate for at least another 15,000 hr?

c. Evaluate and interpret its meaning.

Problem 71E

The average time until a computer chip fails (see Exercise 70) is . Find this value.

Electronic chips Suppose the probability that a particular computer chip fails after t = a hours of operation is .

a. Find the probability that the computer chip fails after 15,000 hr of operation.

b. Of the chips that are still operating after 15,000 hr. what fraction of these will operate for at least another 15,000 hr?

c. Evaluate and interpret its meaning.

Solution:

Step 1

To find the probability that the computer chip fails after 15,000 hr of operation.

We need to evaluate the integral ,

Hence the probability that the computer chip fails after 15,000 hr of operation is 0.472.