00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here we're going to discuss about the binomial distribution.
00:10
Let me remind you that even the x that followed by the binomial with the n and the b and then we can approximate the x by the normal with the mean equal to n times b.
00:23
The standard division equal to the n times b times 1 minus b taking the square root.
00:29
Now, we are given the x, it will follow by the binomial.
00:35
With the n, it will equal to 1000, b equal to the 0 .156.
00:42
And therefore, we can approximate the x into the formula normal, where the mean equal to n times b will equal to the 560, and the standard division is equal to the 560 equal to and then taking the square root equal to the 15 .697.
01:09
And now the question asks, let you find the probability that the x will be between the 570 to the 650 both included.
01:20
It means that we have to equal here.
01:23
Now we need to consider the correction, continuity correction.
01:28
It means that i will have to write this down into the probability that x will be between.
01:33
On the left i have 2 minus the 0 .5 on the right have 2 plus a z upon 5 and then again the 570 .5 on the right have the 650 .5 and now we know that for the normal it will turn the x minus the mean of a standard deviation and tend the standard normal.
01:52
Therefore i need to convert the x into the z by formula in this formula so i will get equal to the 570 .5 and minus the mean will be the 560 over the standard deviation 15 .67 and do the same thing for the right minus the mean over the 15 .697 and then when we compute we have the z it will be between the 570 .5 minus 560 divided by the 15 .697 equal to the 0 .67...