Using the expected value of the binomial distribution, it is found that the robot would be expected to find 19 flawed in a batch of 95 bulbs.
For each bulb, there are only two possible outcomes, either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, 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 is given by:
[tex]E(X) = np[/tex]
In this problem:
- Out of 12 + 48 = 60 bulbs, 12 were flawed, hence [tex]p = \frac{12}{60} = 0.2[/tex].
- A batch of 95 bulbs is taken, hence [tex]n = 95[/tex].
Then, the expected value is:
[tex]E(X) = np = 95(0.2) = 19[/tex]
The robot would be expected to find 19 flawed in a batch of 95 bulbs.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/26155596
