Question

A factory robot recently examined some bulbs, of which 12 were flawed and 48 were not. Considering this data, how many flawed bulbs would the robot be expected to find in a batch of 95 bulbs?

Answer 1

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:

$E(X) = np$

In this problem:

• Out of 12 + 48 = 60 bulbs, 12 were flawed, hence $p = \frac{12}{60} = 0.2$.

• A batch of 95 bulbs is taken, hence $n = 95$.

Then, the expected value is:

$E(X) = np = 95(0.2) = 19$

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 brainly.com/question/26155596