WEBVTT
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Okay, So what we're looking for is the probability
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that a random number lies within two standard deviations of
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the mean and refining it for any normal distribution.
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So I'll just draw out a normal distribution just so
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we can look at it. And that's kind of
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what it's gonna look like. And this will be
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the mean and we want two standard deviations to left
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into the right. Okay, so there's multiple ways
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of doing it. This the first way is to
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know that in any normal distribution 90 approximately 95% uh
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, the numbers are gonna fall within two standard deviations
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. So since we're looking for the probability, that
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would just translate to 0.95 But that's not super specific
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. So if you want on answer that goes to
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more decimal points. You want to be a little
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more specific with it. You can use the Z
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score, and so Z score equals the, um
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, your value. So we'll just call that X
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minus the man over the standard deviation. So we
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know that the value is to ST's, which were
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those away from the mean. So no matter what
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, it's just gonna be two standard deviations, and
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we can just call the means zero, because it's
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for any distribution. And so the standard deviation just
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cancels, leaving you with a Z score of just
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two. And if you have something called table A
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, you can look it up online, and it
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will show you all of the, um, corresponding
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um proportions for Z score of two so you can
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use that and you'll get around. You will get
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around 9545 and that is in decimal form because it's
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a probability, and so that is your more exact
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answer.