## Empirical or 68-95-99.7 Rule Calculation

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There might be something you have to write down calculator steps but I'll tell you when that happens okay so going back to the same problems we just looked at all right don't let fold a wall of them or not but let's just take a look at a couple of them I'll show you how it works all right so if you're working with a ti-84 calculator and I do recommend that even in Delta math there's a calculator app in there but honestly this is so much easier to use you know I think I'm gonna have trouble with math can I move my picture out of the way yeah okay so all right so where do you want to go to work with these problems with this you're gonna use second write that down distribution that's the VAR s button right here okay.

Now there's two that look a lot alike right here there's normal PDF and normal CDF you're always gonna be using normalcdf so it's always number two okay we're picking that one all right now here's some language here that I need to talk about I don't think that mu is very confused and we know what the standard deviation is I mean that standard deviation what the mean is this right here we know what Sigma is this right here but this upper and lower bound stuff I should talk about okay so lower bound is always left on the curve the number line okay as reading left to right it's always left upper bound is always right you cannot reverse that or it'll give you an error notice right here.

I've got mine in the default setting is saying negative 199 remember that's a scientific notation this calculator uses on negative 1 times 10 to the 99 power so that's essentially negative infinity so write this down I will paste it right here for you come on about the calculator language all right so write this down negative infinity is negative 1 be 99 positive infinity is 1 e 9 9 and that's what you can use and that's what was the default in there so I would use it um let me show you what they're talking about okay so technically this curve goes infinitely in both directions right from positive from you being 0 it will go to positive infinity and negative infinity that way now of course the area gets really really small out here past 3 standard deviations but it will still work with using infinity you could probably use like negative 10 and positive 10 and probably get really really really close to the same numbers.

You'll know that's the notation and that's what they're using okay all right so let's go back to the problem and we got everything pulled up here and this one says players way between 178 and 194 so your lower bound is your 178 your upper bound is 194 mu is 178 and Sigma is 8 and we're gonna paste it and hit enter and there's that 47.7% right there so it gives this gives you areas under the curve okay and let's just do one more so this video don't get too long here let me pick a good one here let's see I'm at most that's a good one because this isn't in between two numbers that you know of right this is a good one to do so let's try this one arm it's a second back to distribution number two all right now let's see we got the same mean and standard deviation.

I don't need to change that but I've got deal with my upper and lower bounds and what are they saying so when we earlier we said at most 170 means from the left would be negative infinity up to 170 so this is a spot where you would need to do the negative one second e 99 that's your negative infinity and now your upper bound is going to be 170 and that should give us the number we were looking for now my experience in the past watching people do this and get them messed up is they get confused with positive infinities and negative infinity and you're gonna have to keep it in your mind you get looking at a number line and your negative infinity is always on the Left positive infinity is always on the right so if you're taking everything to the right side of the curve you're gonna be dealing with a positive infinity and if you're taking stuff to the left a negative infinity so let's hit enter here and see what happens and there's that 0.159 that we got earlier so as you can see it's a powerful tool this comes up in the next lesson anyway so don't mind showing you this use this and hope it helps those are used smart of to watch this video all right I'll see you in the next one

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