WEBVTT
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okay for this problem, we're gonna talk about some
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likelihood or some probability of my i Q scores.
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So the biggest fact we're going normal applications in this
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chapter. So we're told that's normally distributed with a
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mean of 100 and a standard deviation of 16.
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Okay, I said no. That's to me.
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The 100. And if we got rid of 1
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16 we have the next one over there. If
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we went down one standard deviation, uh, be
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down to before. So that's like some rough boundaries
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here you could schedule over now, but let's just
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look at plus or minus one standard deviation roughly.
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And then what I like to dio and I think
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your teachers want you to do is to show the
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direction with what you have. So let's restate what
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we want. It's always good to restate using probability
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notation what you want. So for part A,
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they specifically asked you the likelihood that you have scores
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between 120. So the way you write the probability
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rotation is the probability that you have scores between 101
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20. It's always a good idea to show that
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direction so 100 is here went when he just passed
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there. So I left in space here just to
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do this. So not the most beautiful sketch,
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but the sketches for direction. You're not sketching a
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graph to be grated. So 101 20 is that
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chunk there? So you have a decent size number
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, but not a huge number for the probability.
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Now you look at table three and like a disease
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course reach of those and they get the probabilities or
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a more efficient way to do this is to use
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a calculator. Workers APP lets you need to use
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normal CEO cumulative density frequency. So calculators gonna want
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you to say worried. Look, So you're telling
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the calculator Well, I want to look from 100
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to 101 120 for this problem. So 100 is
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my lower boundary and my upper boundary Is that 1
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20? Um, and I take this in a
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minute ago. But if you don't have this year
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, 100 is my mean and my standard deviation.
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So everything matches what's on my calculator? I think
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much of my diagram teachers replied. Rather see the
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diagram. I don't even see a calculator, but
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let's get the probability of that 0.394 that seems to
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make sense. Based on the relative size of the
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distribution of the area. Under the curve is always
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one for everything. 10.394 39.43 percent is the likelihood
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of that score. Not for part B. Let's
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look at this party Wants to know, uh,
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the likelihood that your score over 80 Okay, it's
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we're going to say X is greater than he.
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This is a pretty big numbers of 80 Force here
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, once in a deviation below 80. Would be
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about right here, brought up here for reference.
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Um, so I'm gonna little overlapping sketching here,
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but it's all right. So over 1 80 So
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what really happens here? He's really looking at a
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relatively big number because it's the whole area under the
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curve. So everything above 80 so should have a
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pretty big number. So let's go to our calculator
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and see what we got. So we're gonna find
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the distribution of the scores. It's normally distributed him
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since we've been told that, um, human live
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Lee looking left to right. So after, right
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, we know 80 is the lowest point that we
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concerned with for this problem, and we want to
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go to infinity. And 99999 is perfectly fine for
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the relative size of the numbers. The mean is
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100. This an innovation 16. So it's gonna
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give us the area to that curve with proportion,
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no scores of all in that area. So we
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have a number. It's pretty big, great ones
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, the whole thing. So that says about 89%
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890.89 for three for four do around in there.
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So the probability that we get scores that a greater
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than 80 is pointing nine for four.