How Safe Are You? Assume one of your favorite activities is mountain climbing. When you go mountain climbing, you have several safety devices to keep you from falling. You notice that attached to one of your safety hooks is a reliability rating of 97%. You estimate that throughout the next year you will be using this device about 100 times. Answer the following questions.

1. Does a reliability rating of 97% mean that there is a 97% chance that the device will not fail any of the 100 times?

2. What is the probability of at least one failure?

3. What is the complement of this event?

4. Can this be considered a binomial experiment?

5. Can you use the binomial probability formula? Why or why not?

6. Find the probability of at least two failures.

7. Can you use a normal distribution to accurately approximate the binomial distribution? Explain why or why not.

8. Is correction for continuity needed?

9. How much safer would it be to use a second safety hook independently of the first?