Digital Clocks: Binomial Problem Analysis and Results

  • MHB
  • Thread starter Math101_McF
  • Start date
  • Tags
    Binomial
In summary: That is the probability that at least one of the clocks is defective, which is $\begin{pmatrix}0.9 \\ 1\end{pmatrix}(0.95)^{74}$.
  • #1
Math101_McF
2
0
A company makes digital clocks. It is determined that 5% of all clocks produced are defective.

you go to the warehouse and randomly select 80 clocks.
1. How many of the 80 clocks do you expect to be defective?

2.What is the probability that exactly 6 of the clocks are defective?

3. What is the probability that at least one of the clocks (out of 80) is defective? use the complement.
 
Physics news on Phys.org
  • #2
Hi there,

Welcome to MHB! :)

We like to tackle one problem at a time. Which one do you want to look at? What are your thoughts on it?
 
  • #3
1
 
  • #4
Math101_McF said:
1
Ok so we really want to help you but won’t give you answers. If you show what you’ve done we will do a ton to get you to the finish line but if you want answers for free this isn’t the place.

What we do have here are volunteers with PhD’s, other advanced degrees, and years of experience teaching math. We actually want you to like math and learn. For free. Promise.
 
  • #5
The answer is almost given in the question:
"A company makes digital clocks. It is determined that 5% of all clocks produced are defective.

you go to the warehouse and randomly select 80 clocks.
1. How many of the 80 clocks do you expect to be defective?"
5% of 80 is (0.05)(80)= 4.

"2. What is the probability exactly 6 clocks are defective."
Each clock is either "defective" or "not defective" so this is a "binomial distribution". There are 80 clocks. The probability any given clock is broken is 0.05 and the probability it isn't is 0.95. The probability exactly 6 out of 80 are broken is $\begin{pmatrix}80 \\ 6\end{pmatrix}(0.05)^6(0.95)^{74}$.

"3. What is the probability that at least one of the clocks (out of 80) is defective? use the complement."
The opposite of "at least one" is "none". Calculate the probability that none of the 80 clocks is defective, $(0.95)^{80}$ and subtract that from 1.
 
Last edited:

Related to Digital Clocks: Binomial Problem Analysis and Results

1. What is a digital clock?

A digital clock is a timekeeping device that displays the time in numerical form using digits or numbers. It is powered by electricity and usually has a built-in microchip that keeps track of time.

2. How does a digital clock work?

A digital clock works by using an electronic oscillator to generate a steady stream of pulses. These pulses are then counted and converted into hours, minutes, and seconds by a microchip. The numbers are then displayed on the clock's screen using a digital display such as LED or LCD.

3. What is a binomial problem analysis?

A binomial problem analysis is a statistical method used to analyze data that follows a binomial distribution, where there are only two possible outcomes (success or failure). It involves calculating probabilities and using statistical tests to determine the significance of the results.

4. How is a binomial problem analysis used in digital clocks?

A binomial problem analysis can be used in digital clocks to analyze the accuracy and reliability of the clock's timekeeping. By conducting experiments and collecting data on the clock's performance over a period of time, the results can be analyzed using binomial problem analysis to determine the probability of success (accurate timekeeping) and identify any potential issues.

5. What are some common results found in binomial problem analysis of digital clocks?

Some common results found in binomial problem analysis of digital clocks include the average accuracy of the clock, the probability of the clock being accurate within a certain range of time, and any potential patterns or trends in the clock's timekeeping. These results can help identify areas for improvement and inform the design and production of more accurate digital clocks.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
17
Views
1K
Replies
1
Views
709
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
8K
Replies
2
Views
2K
  • Electrical Engineering
Replies
26
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
984
  • Set Theory, Logic, Probability, Statistics
2
Replies
41
Views
4K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
3K
Back
Top