Question

Interpretation Suppose you are a hospital manager and have been told that there is no need to worry that respirator monitoring equipment might fail because the probability any one monitor will fail is only $0.01$. The hospital has 20 such monitors and they work independently. Should you be more concerned about the probability that exactly one of the 20 monitors fails, or that at least one fails? Explain.

Name: Problem 5, Chapter 5: Understandable Statistics Concepts and Methods
Uploaded: 2021-04-10T05:46:41-08:00
Duration: 2 min 15 s
Channel: Manisha Sarker

   Interpretation Suppose you are a hospital manager and have been told that there is no need to worry that respirator monitoring equipment might fail because the probability any one monitor will fail is only $0.01$. The hospital has 20 such monitors and they work independently. Should you be more concerned about the probability that exactly one of the 20 monitors fails, or that at least one fails? Explain.

Understandable Statistics Concepts and Methods

Charles Brase,… 12th Edition

Chapter 5, Problem 5

Instant Answer

Solved by Expert Manisha Sarker

04/10/2021

Step 1

This is a binomial probability problem, where the number of trials is 20 (the number of monitors), the number of successes is 1 (one monitor fails), and the probability of success on each trial is 0.01 (the probability that any one monitor will fail). The binomial Show more…

Show all steps

Thanks for your feedback!

Interpretation Suppose you are a hospital manager and have been told that there is no need to worry that respirator monitoring equipment might fail because the probability any one monitor will fail is only $0.01$. The hospital has 20 such monitors and they work independently. Should you be more concerned about the probability that exactly one of the 20 monitors fails, or that at least one fails? Explain.

Play audio

Feedback

Manisha Sarker and 62 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Binomial Distribution

The binomial distribution describes the probability of having exactly k successes (or failures) in a fixed number of independent trials, where each trial has the same probability of success. In this context, it allows us to calculate the probability of exactly one failure among multiple monitoring devices.

Complement Rule

The complement rule helps determine the probability of at least one event occurring by subtracting the probability that the event does not occur at all from one. This is particularly useful for finding the chance of at least one failure across several independent devices.

Independence of Events

In probability theory, when events are independent, the outcome of one event does not affect the outcome of the other, allowing for the joint probability to be calculated as the product of individual probabilities. This principle underlies the computations of failure in multiple monitors.

Please give Ace some feedback