00:01
This problem says suppose that 10 % of all steel shafts produced by a certain process are non -conforming but can be reworked rather than having to be scrapped.
00:09
Consider a random sample of 200 shafts and let x denote the number among those that are non -conforming and can be reworked.
00:14
What's the approximate probability that x is at most 30, less than 30, and between 15 and 25 inclusive? and to find these probabilities we're going to treat this as a binomial distribution where we have a probability that's considered success or failure.
00:26
Either we are going to be non -conforming and can be reworked or we're not.
00:30
And also we have independent events for these certain steel shafts.
00:34
So for a, b, and c we're going to use binomial cdf in our calculator because we want cumulative probabilities.
00:41
And for a we want the probability that we are at most 30, which means less than or equal to 30.
00:46
And for binomial cdf we start off with the n value and p value of our distribution.
00:52
And here we had 200 in our sample with the probability p value of 0 .10 from 10%.
00:56
And then we list the lower bound and upper bound that we want the probability between.
01:02
And here we want to be less than or equal to 30, so 30 is included for the upper bound.
01:06
And the lower bound would be the lowest possibility of the 200, which would be 0...