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All right in this video I'm going to talk about the normal distribution and what I'm going to talk about is what's known as the 6895 99.7 rule for normal distributions or bell curves and what it says if you have a normal distribution with a mean mu and a standard deviation of Sigma it says the bulk of your observations which in this case 68% of the observations are going to fall within one standard deviation of the mean mu it says ninety-five percent of your observations are going to fall within two standard deviations of the mean mu, and it says ninety-nine point seven percent of the observations will fall within three standard deviations of the mean mu so lets uh let's try to make some sense out of that, so there's a popular IQ test, and it turns out that the scores for these IQ tests are approximately normally distributed with a mean of 100 and a standard deviation of 15 we're going to use the 68 95 99 point 7 rule to figure out the following, so we're going to do three things we're going to figure out about what percent of people have IQ scores above 100 above 145 and below 85, so I went ahead and made a little normal distribution here pretty rough again the peak is where the mean is, so we know the means at 100 that's given to us, so the first question is you know about what percent of people have a score above 100 well again the idea for a normal distribution 50% of the observations roughly are going to be you know at or below the mean and again roughly about a hundred fifty percent of the observations are going to be at or above the mean so in this case since our mean is at 100 we know that 50 percent of the observations are going to be to the left 50 percent of the observations are going to be to the right so to answer Part A we don't have to do much at all we don't have to really use this rule so above 100 again half the observations will be you know roughly again half the observations will be below 100 half of them will be above 100, so I would say we'll say about 50 percent so about 50% of the observations would be above 100 the second question was what about above 145 you know what percent of the observations and this is where we're going to start using our rule and let's go ahead and talk about it on this example anyway, so our standard deviation was 15, so I'm going to add 15 to 100 that will give me 115, and I'm also going to subtract 15 from 100 that would give me 85 and again what this rule says is we're now one standard deviation away from the mean this is supposed to be symmetric, but it's you know obviously I'm doing this by hand so not quite perfect what we could conclude here is we could actually say, and we didn't ask this question at all, but we could say roughly or approximately 68% of the IQ scores are between in this case between 85 and 115 okay, so we've gone one standard deviation away if we go two standard deviations away okay so if I go two standard deviations I'm going to have to add another 15 that's going to put...
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