Hello and welcome to a video on probabilities in Excel. Today we'll be talking about a very specific
type of problem-using probabilities where we're finding the area under the curve in a normal distribution.
So the problem sounds something like this. In a normally distributed distribution with a mean of 80 and
a standard deviation of 12, what is the probability that a randomly selected score will fall below 92?
So here we have a bit of a visual aid and this one's it's not a perfect aid. I got it from another website and
I don't really like the way it's set up, but we'll deal with it. Our mean here is 80. Our standard
deviation is 12 but that's not reflected in the tick marks down here so don't use these as a guideline.
And our x-value is 92 right here on this dotted red line. And what we want to know is
if we randomly select an x-value from this distribution, what are the probability?
What is the probability that it will be in this blue shaded section? So to find the probability
below something, we use equals norm dot dist d-is-t,
open parentheses. And you can see here x-l is prompting us through
some values for our arguments in these parentheses. So the x-value
is 92, because we know that's our randomly selected, or where we would like to find below our randomly
selected score. That's our x-value. Our mean is 80. Our standard deviation
is 12, and cumulative percent is always true. Now I'll hit enter,
and we get 0.841345. So we have an 84% chance, roughly,
of landing below 92 in this distribution. And we can see that that makes sense, because most
of our distribution is to the left of 92. So what if we wanted to find the probability
of landing in the white section of this distribution? Well to do that, we use equals
1 minus norm dot dist, where our x value is still
92, the mean is still 80, and we have a standard deviation
of 12. And we see the probability of above
is 0.158655. Now we did 1 minus norm dot dist, because we know
that this whole distribution equals 1,
and we can test this by adding the two of these together,
and they come out to 1. So we know
that these are the totality of this distribution. Now, remember with probability, you can't
have a number greater than 1, and you also can't have a number below zero. So if you're ending up with negative results
on these problems, you have done something in correct or backwards, and if you are getting a
total or in value greater than 1, then you have also done something in correct or backwards. I've
never seen someone get a value greater than 1, unless they were trying to add probabilities
together somehow, in a way that didn't make sense. So, if you're getting something
like that on your homework and you're not really sure what's happening, reach out to either your instructor or if we have
tutors that semester, reach out to a tutor, and see what's going on. Okay, let's move on to the next
kind of question. What is the probability in a normally distributed distribution of selecting
an x value between 54 and 78 with a mean of 70 and a standard deviation of 8? Okay,
once again, we've got a little visual aid here, our mean is 70, and we would like to find values between 54
and 78. So to find a probability between 2 values, we're actually going
to subtract 1 value from the other. We're going to take the smaller value and subtract
it from the larger one. Now the reason this works is because we want to subtract this white space
here from this space here. So if I were to find the probability below
78, it's going to return all of this, including this little white bit and this blue bit.
And if I were to return below 54, it would just return this white bit. So we want to subtract below
54 from that. So let's go ahead and see what that looks like. So we're going
to do the same norm.dist. We're taking our larger number first.
So 78, our mean is 70. Our standard deviation is 8. And cumulative percent is
always true. From that we are subtracting norm.dist 54,
70, 8, true.
Okay, and we've got our probability of landing between those two scores is 0.818595.
So that's about 80 percent, or 82 percent, of our distribution is landing
between these two scores. And that makes sense when we just visually look at it. So what if we
wanted to find the probability below 54? What we do at the same way we did before,
by using
our norm.dist, our x-value, our mean, our standard deviation,
setting cumulative to true.
And our probability of above, and we can see this is a very small number, which makes sense. It's a very small part of our distribution.
And the probability of above, remember,
is equal to 1 minus norm.dist. And this time we want
above 78, because we're looking for that other white part of the distribution. Okay,
and now the same is before.
When we totaled up, remember when we totaled to these two up, they equaled 1. If we were
to add at these three values, they
will also equal
1. So this whole distribution will always be equal to 1.
Okay, we have another type of problems that you will be encountering on your homework. Let's say
we have a clinic that wants to identify patients who score low on a test, so that the patients can be offered
a new therapy. The scores are normally distributed with a mean of 80 and a standard deviation of 12. The
clinic decides to find the lowest 40% of scores. What is the score that marks the 40th percentile?
So here, we're not looking for a probability. We're actually looking for an x-value
using a probability score. So to do that,
we're going to use norm.inv, which is the inverse. And for that,
we're going to need to give it probability. So the first argument here will be probability.
We know that it's 40%, so that is 0.00.
And then the mean is 80. And the standard deviation is 12. And here we don't have to worry about telling
it that the cumulative percentage is true. Okay, so we know our x value is 76.95983.
Okay, that's all you need to know about probability and finding an x value given
a percentile. And let us know if you need any help with your homework and we're happy
to help.