00:01
So we're told a machine processes parts one at a time, and the processing times, we'll call those x, measured in minutes, are independent random variables, and they're uniformly distributed with a lower bound of five up to 15.
00:21
So this means it'll take as little as five minutes, up to the maximum of 15 minutes per part.
00:27
And we wanna know the probability that the number of parts processed in eight hours is at least 100.
00:34
So that the number of parts processed is greater than or greater than or equal to 100.
00:48
So let's think about what we have here.
00:52
So this is the processing time.
00:59
Processing time, all right, is, for one part is five to 15 minutes, uniformly distributed.
01:07
So the least amount of time is five, the maximum time is 15.
01:13
Oops, number of, i need to add a qualifier here.
01:15
Number of parts processed in eight hours.
01:19
That's a key thing here.
01:21
And so how many, well, how many minutes are in eight hours? let's see, eight hours times 60 minutes per one hour, little unit conversion, hours cancel out, eight times 60, you have 480 minutes in eight hours.
01:41
So this is how many minutes there are in eight hours...