00:01
At a company that manufactures widgets, it is known that 1 out of every 43 widgets is defective.
00:08
So, that's a probability of 1 over 43 for any randomly selected widget.
00:13
And we consider a batch of 237 widgets that are produced, and we want to find the probability that fewer than 5 of the widgets in the batch are defective.
00:25
So, let's first define a random variable, x, as the number of defective widgets in the batch of 237.
00:33
In this scenario, each of the 237 widgets can be thought of as bernoulli trials with two outcomes of interest, either defective or not.
00:42
And if we can assume that their outcomes are independent, and the probability of being defective for each widget is 1 out of 43, then the number of defects and the fixed number of independent bernoulli trials is a binomial random variable.
00:57
So here, x is a binomial based on 237 trials, and a 1 over 43 probability success on each trial...