00:01
In this question, we're given that 5 % of worm gears produced by machines defective, and 6 gears are randomly selected.
00:09
I'm going to let x be the number of gears out of 6, which are defective.
00:14
Now, x actually follows the binomial distribution.
00:17
Let's see how it is so.
00:19
Now, the binomial distribution has four criteria.
00:22
The first criteria, the number of trials, n is fixed and are identical.
00:27
Now, in this case, we're looking at 6 gears, so n is six.
00:31
And the trial is that we are looking at the gear whether it is defective or not.
00:36
So this experiment or this trial is identical for all the six gears.
00:42
So the criteria one is fulfilled.
00:44
For the second criteria, each trial experiment is independent.
00:49
So each of these six gears, whether they are defective or not is independent each other.
00:53
So criteria two is fulfilled.
00:56
Third criteria, each trial results in one of two outcomes.
01:00
Success and failure.
01:02
So for each gear the success is it is defective and the failure it is that it is not defective.
01:09
So the criteria is fulfilled.
01:12
Last criteria, the probability of success denoted by p is the same for each trial.
01:20
So in this case, this 5 % is the probability of success in that sense, probability of a gear being defective.
01:30
It's 5 % percent.
01:30
And this is assumed to remain the same for each of this gear.
01:36
Now since this 5 % is like an overall survey or overall data collected for the general population of all the gears.
01:45
So this is assumed to hold constant for all the gears.
01:49
So criteria 4 is fulfilled...