Respuesta :
Answer:
mean: 10 chips
standard deviation: 3.1 chips
Step-by-step explanation:
From Khan Academy, I know you guys just want the answer so there it is :)
Using the binomial distribution, it is found that:
- The mean number of defective processing chips in these samples is of 10.
- The standard deviation is of 3.1.
For each chip, there are only two possible outcomes, either they are defective, or they are not. The probability of a chip being defective is independent of any other chip, hence the binomial distribution is used to solve this question.
What is the binomial distribution?
- The binomial distribution is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
- The expected value of the binomial distribution is given by:
[tex]E(X) = np[/tex]
- The standard deviation of the binomial distribution is given by:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
In this problem:
- 2% of the chips produced are defective in some way, hence [tex]p = 0.02[/tex].
- A quality check involves randomly selecting and testing 500 chips, hence [tex]n = 500[/tex].
Hence:
[tex]E(X) = np = 500(0.02) = 10[/tex]
[tex]\sqrt{V(X)} = \sqrt{500(0.02)(0.98)} = 3.1[/tex]
The mean is 10 and the standard deviation is of 3.1.
To learn more about the binomial distribution, you can take a look at brainly.com/question/26155596
