WEBVTT
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okay for this problem were given some human resource data
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about salaries, um, and jobs. So annual
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salaries for this job, you're supposed to be on
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average,$76,503. And the variation or, um
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, or school precisely. The standard deviation from this
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2007 data says, uh, well, salaries go
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up down, or the typical deviation from the mean
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is 80$8850. Okay, as with any problems
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, probably kind of sketch out what it looks like
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that's normally distributed on what we're doing with this problem
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is really what is looking at some likelihoods of what
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occurs, um, be single value and the probability
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of something occurring for ah, or the sample mean
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? So let's look at this for the single values
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. So what's the probability of gonna translate this right
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into our probability notation? So we could say,
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What's the probability that the branch that the human resources
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person there is over 100,000? All right, so
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let me like to draw. It kind of gives
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you a general idea. So really, if this
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is about$76,000 for the sample mean, uh,
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$100,000 is gonna be way over here, so it's
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gonna be way after the side, so the probability
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is pretty likely that a single person does, but
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it's possible. So let's see what it is that
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these are calculated. We've done enough of these.
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Now that we're gonna take a look and let the
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calculator look at our distributions, we know it's a
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cumulative density frequency. So, uh, so we
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know we're looking from the lower boundary of$100,000 to
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infinity. We're looking about that's like to draw it
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out. So we kind of see that we're going
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this. What s represented is what's on the red
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on the screen. We know the mean for this
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problem. We've been told the data tells us the
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mean salary is five or three, so that$100,000
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salary is much higher and standard deviation a typical variation
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. There is only Colony 150. So pretty big
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wish over here to get that salary based on the
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averages at least. So let's see what we get
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. So and it is a small number, as
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we kind of expected. So the likelihood of that
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is, uh, 0.39 So I'd say the 0.4%
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chance that you get that. Have a salary if
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the average is supposed to happen in between those two
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. Okay, so now and it just mark this
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up a little bit better now. So 76 1000
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for party. We want to know that, Um
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, what's the What's the odds of the sample mean
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? Salary of this branch falls between what's expected there
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. So you can also put the sample mean up
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there. So now we're looking between I'm gonna save
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a little bit of digits. Space years. So
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the sample mean between 70,000 and 80,000 Some scar,
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right, Kay? Okay, 17 80 k So
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76 is there. We know that 70,000 and 80
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thousands of nice little slice of the middle here,
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so we should get a mush higher number. And
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that's what we're trying to figure out. So,
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um, industry in this up. So and we'll
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make sure ever good notation of the probability that it's
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between 70 and 80,000. Party. So we're gonna
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use our distribution from a calculator and one of the
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thing here too. I think I need to write
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down and will be get blue. Just emphasize it
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. That's based on a sample size Russia gonna sample
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on average 20 human resource managers. So that's instead
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of having a single person up here just for reference
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here in just a single sample or one person never
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turn about 20 people. Um, so let's see
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what we get. So go back to our distribution
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normal CDF and we're looking at a much more representative
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sample here between 70 and 80,000. So it's put
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in 70 and 80 upper bound, and we know
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that means should be 76,000 right in the middle.
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And we've been told that the salary variation 8 50
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is, uh, a little steak there. It's
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not 76,000 middle. It's 76,503 alone. Okay,
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so let's see, uh, almost people mistake there
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. So it's not just this, and the key
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part of the problem is we take our standard deviation
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and we divided by the square root of the sample
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size cause that impacts our outcomes. So it's the
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square root of 20 you taking your 8815 divided by
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the square 20 your teachers picky about that? You
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can show that off as a separate calculation and we'll
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see. That's much higher. Likely that especially the
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30 if you sample 20 there. So in the
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end, we know the probability is 96% about so
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the probability that you haven't mean that exists between 70
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and 80 given 20 samples. ISS 0.961