00:01
Okay, so let's define x as the number of defectives, and that's in the batch of 250.
00:24
So, x is approximately equal to the binomial 250, comma, 0 .05, and we can approximately x by a normal distribution.
00:49
So since np is equal to 12 .5, which is greater than or equal to 10, this case it's greater than, the mean and standard deviation of x is the following.
01:21
So the mean is 12 .5 and the standard deviation is 3 .446.
01:40
If we consider the fact that 10 % of 250 is 25, we could now figure out this probability, probability of x being greater than or equal to 25 is equal to 1 minus the probability of x being less than 25, which is the same thing as 1 minus the probability of x being less than or equal to 24 .5.
02:32
And this is approximately equivalent to the following.
02:50
And now we could simplify this even further to get the following and our final answer would be 1 minus 9997 which is equal to 0 .0 .03 and the exact binomial probability from the software given in the textbook is .006.
03:41
So either one of these works.
03:43
Again, these are very small numbers.
03:45
So this might seem like it's a big difference, but they're very, very close to one another.
03:50
So this is a, and now for b, we're using the same normal approximation with the continuity correction.
04:05
So we have the probability of x equal to 10...