# Digital Clocks: Binomial Problem Analysis and Results

• MHB
• Math101_McF
In summary: That is the probability that at least one of the clocks is defective, which is $\begin{pmatrix}0.9 \\ 1\end{pmatrix}(0.95)^{74}$.
Math101_McF
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.

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Math101_McF said:
1
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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:

## 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.

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