Question. We're using an airline example and we're having that the probability of a no show is 16%. And we're having what happens on the next 42 reservations. And again, assuming Lee that these reservations are each independent begin. And we know that that's not really a justifiable situation because you have people that go together in pairs or families that travel together or business people that are traveling together. And if we find N times P, we find that end times B. Which would be the mean of our distribution is equal to 6.72 And I happen to store that in my calculator as alpha A. That would just be helpful for me later on. And the standard deviation of that distribution is a square root of N times p times one minus P. And I did that calculation and I got 2.376 And I happened to store that in my calculator as X. Just so I don't have to type all that. And again, so when I write them down, I'm going to refer to him with those letters. Now we know that N. Times P and end times one minus P. And the one minus P would be that 10.8 for their both greater than a wrinkle to five. So this distribution is approximately normal, centered at 6.72 With this standard deviation, I could draw the picture of the distribution, but we have quite a few things we want to find And we want to know what's the probability if 42 reservations are made, what's the probability that there are exactly five, no shows. And so to do that normal uh that continuity correction and find this with a binomial excusing with the normal probability, we need to go half a unit below four point 5.5 a unit higher 5.5 and find that area between those two numbers. To use the normal approximation. Now we need to convert these two Z values and I'm going to write this one down and then I won't won't write down all the rest. We have 4.5 minus are mean provided by our standard deviation and then that will be a Z value and then we'll take that 5.5 minus are mean and then divided by our standard deviation and let me quick do that on my calculator here. So I have that 4.5 minus four mean, which I stored as alpha A divided by the standard deviation. And that Z value rounds to a Z value of negative 40.93 Mhm. And then the other z value which again I can just arrow back up and change that 4.5-5.5 I get negative .51. Now, I'm going to end up using my normal CDF with these two values, you can also use your table very easily and look up But negative .93 would be my low number and negative .51 would be my upper number and leave my mean and standard deviation 01 respectively. And when I do that I get .1288. You can look these values up in your table as well, defend that area between next we want to find from uh nine people out of the 42 all the way up to 12 people and it says inclusive. So we want to include those values now For using the continuity correction. This needs to bump down to 8.5 and this one needs to bump up to 12.5 and then I'm going to do that same calculation right here, just substituting 8.5 and 12.5 in of those values. So let's see what we get for the Z values. So let me just arrow back up And we will change that value to an 8.5 And that z value becomes .75 .75. Is that CLUCR 3/4 of a standard deviation higher than the mean. And this 12.5. Let me do a little insert there to get that value in 12.5 And that's the value becomes 2.43. Now, once again, you can look those values up in your table. I'm going to use my normal CBF to find those values and I'm going to use this .75 as the lower and there's 2.43 as the upper And then find that area between. And that comes out to be .2191. And likewise you can look those values up in your table. Part C. Now we want to find the probability that at least one no show. Well in order to calculate that as a Z. value again we are going to use the continuity correction and that means I have to go down .5. so we're going to use 0.5 and use that value in place of our 4.5. So I can go up in do that little change and we want zero wait five. That's the value. I'll leave it in blue. Nice to see a color different black all the time Is negative 2.62. And then you can look that up in the table. But remember you are finding a value that here is negative 2.62 and you're finding this. So if you're gonna look it up in the table, it's actually easier to look up positive 2.62 and find the area below And positive 2.6. To looking it up on the table, I get .99 56 And now we're almost done. We have one more to do. Let's go green. And we want to find the probability that at most two now for our continuity correction, we need to bump this up. So this is what we'll use in place of uh this value right here and we'll convert that to a Z. Value. So let's find out what that Z value is. So I just have to arrow up, Change that to a 2.5. And we get that Z value Is negative 1.7 and that would round to eight. So I'm just going to click look that up in my help and my table and not using my software. And when I do .8 that comes out to be .0375. Mhm. And I think we're all done. Yeah.