00:01
Hello and welcome back to statistics.
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We have a short three -part problem, so let's get right into it.
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It tells us that for a certain group of individuals, the average heart rate is 71 beats per minute.
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So that's going to be our mu, 71.
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And assume that the variable is normally distributed in the standard deviation is three beats per minute, so our theta, or sigma rather, is going to be three.
00:24
And it tells us that if a subject is selected at random, find the probability that the person has the following heart rate.
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And so there's three parts.
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And we need to round the answers to four decimal places.
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So part one, we need to find that it's between 67 and 73.
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So we'll let our variable be x, which is normally distributed.
00:46
So we need to find the probability that x is between 67.
00:51
So it's greater than 67, but less than 73 beats per minute.
00:56
So to do this, we're going to need to convert to z scores in the top right.
01:00
In green, i have already wrote down the formula to convert any score to a standard normal score or a z score.
01:11
And so we need to find the probability that it is between 63 and 73.
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So this probability in green right here is what we're looking for.
01:23
So of course, step one is going to be the z scores to find the z scores.
01:27
So for 67, so z for the lower bound is going to be.
01:32
67 which is the x bar or actually it's just x in this case so it would just be our average beat permit 67 minus the mean mute which is 71 all over our standard deviation which is 3 and that is going to give us negative 4 thirds and our upper bound will be 73 minus the mean of 71 over the standard deviation 3.
02:09
It's going to give us two thirds.
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So in other terms we can write for 63, our z score is negative four thirds.
02:20
And for 73, our z score is two thirds.
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So we need to find the area between them.
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And to do that, we're going to use a function on our calculator called normal cdf or norm cdf.
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As the calculator calls it.
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So in this function, it's going to ask for a lower bound, which will be our lower z for negative four thirds, and then upper bound, which is our upper z, which is two thirds.
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And of course, it's going to also ask for the mean and standard deviation, which will be zero and one respectively, because now we have converted to a standard normal scores, or z scores rather.
03:01
And so when you do that, you're going to get a probability of 0 .6563.
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So this area here is 0 .6563.
03:12
Now let's go to part two.
03:15
So we need to find the probability that x is greater than 69 beats for a net.
03:23
So x is greater than 69.
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And so now we need to convert this to a z score...