Welcome to Excel 2013 statistical analysis video
number 37.
Hey, if you want to download this PDF or the Excel
files that go along with this video, click on the link
below the video.
Hey, Chapter 6, continuous probability distributions.
We want to remind ourselves where
we came from, Chapter 5 we did discrete random variable
and discrete probability distributions.
Now we're going to move on to continuous.
Now let's remind ourselves of discrete random variables.
Remember there were gaps between numbers one, two, three.
We were mostly counting.
Discrete random variables can only
assume clearly separated values, usually
from counting successes.
We did things like count the number of banquet rooms used,
number of customers arriving at Dick's Hamburgers, number
of times a plane was late, cards pulled from a deck.
Now continuous random variables, hey, there's
no gaps between numbers.
For any two numbers we could have as many possible values
between there.
It depends on the measuring instrument.
The continuous random variable can assume any value
in an interval or collection of intervals.
It depends on the measuring instrument.
Examples, weight of ketchup bottle, salary earned.
Now remember, dollars seem like discrete,
but they're really not because we could chop it up
into partial pennies as fine as we would like
gas prices, scores on test.
Now each one of the discrete and continuous random variables
share the definition of a probability distribution.
Hey, that's a description or presentation
of how the probabilities are distributed across the values
of the random variable.
Last chapter it was discrete random variable,
this chapter it's continuous.
Now we want to really strongly differentiate
between how we did things last chapter
with discrete probability distribution
and how we're going to do it with continuous,
because there's a huge difference.
Now last chapter we talked about binomial, Poisson,
and hypergeometric.
For example, the binomial distribution looks like this.
The height of the columns were both the height
of the column and the probability.
That height represented the probabilities,
and as such we were allowed to say, hey,
what's the probability of exactly one plane late.
In six tries it was 0.35.
That came from the height of this.
We were also allowed to ask hey, what's
the probability that random variable x counting
late planes in six tries was between 1 in 3.
We simply added the height of the columns
or the probabilities to get our total probability.
So guess what?
Last chapter we could calculate the probability for exactly
an x or between two x.
Now Chapter 6 continuous probability distributions
we're going to talk about the famous normal or bell shaped
distribution uniform and exponential distribution.
The normal curve will not have columns.
It will be a plotted curve where it's area under the curve that
determines our probability.
And guess what?
We're not allowed to calculate an exact x.
This distribution will look at this
is salary for accounting positions in Seattle area.
The average or mean for the population is 53,000.
And then we'll talk in terms of x's and z's, which
are standard deviations.
So if we want to calculate the probability of exactly
$50,000 job, we can't do it.
Now the reason comes from the fact
that a line or an exact point has no area.
So this particular model is not going
to allow us to calculate an exact probability.
All we're stuck with is between.
So if I say hey, random variable x,
that's salary of accounting positions in Seattle,
what's the probability of getting
a job between $50,000 and $60,000?
Well, we can go ahead and calculate the area
under the curve using integral calculus
or our Excel functions.
And the probability will be 0.67.
All of this area is probability.
The whole area from negative infinity to positive infinity
is 1.
But the area that we will be calculated is always between.
So guess what?
Questions last chapter, we could actually ask the probability
of exactly an x or probability between two xi's.
Values here, questions you can ask, there it is,
just 1, probability between two x values.
Now let's scroll to our next page talk a little bit more
about why that's true.
Here's for our discreet.
Here's for continuous.
We're going to look at two examples,
the binomial probability function
and for our normal curve, the normal probability density
function.
Now whereas this binomial function
told us the height of the column,
it also calculated the probability
of an exact x value.
This will not do that.
It will however calculate the height of the plotted curve
when we chart it.
But it will not calculate the probability of an exact x.
Both binomials and the normal distributions
can calculate between two x values.
Again, for the binomial, we've just simply added them and got
between two x's.
Over here, we're going to have to do integral calculus,
or we can use one of a few functions,
we're going to see them norm dot dist.
We will give it the lower and upper values,
and it will calculate the probability for us,
do the heavy lifting and do our integral calculus.
And we'll talk more about this two videos ahead.
But I want to emphasize here for our continuous probability
distribution functions for all three, normal, uniform,
an exponential, area will equal probability.
All area will equal 1.
We're not allowed to calculate an exact x.
And the reason why is because if we plot this right here
in exact x, it's a line.
And the area for that line is 0.
So we can actually try, but it's 0.
Not only that, but if we use greater than
or equal to-- so this is x greater
than or equal to 50,000.
That's going to be equal to x greater than 50,000
because the line has no area.
Now let's look at three examples of what we're
going to be allowed to do, one for each one
of our distributions.
For our normal our bell shaped distribution,
we're allowed to ask a question like hey, what's
the probability we could get an accounting
job in Seattle area between $50,000 and $60,000?
The answer will come from the area under the curve, 67%.
Another example-- and this is for our uniform distribution
where we're going to be dealing with a rectangle.
We're allowed to ask a question like what
is the probability that we will wait
on hold on the phone for customer service help
between 15 and 20 minutes?
The answer will come from area determined by width and height
calculation.
We'll find out that the probability is 0.25.
And finally, for our exponential distribution
we're allowed to ask a question like what
is the probability that you will have
to wait less than 15 minutes in a Disneyland line?
The area or probability will come from the area
under the curve.
The answer will be 0.49%.
All right.
So we get the idea it's always going
to be between two x values and it's
going to be area, which is probability.
Now an important note about Chapter 6.
In Chapter 6 we'll be dealing with population data
that make up the distribution, so mu and sigma,
mean of the population, standard deviation of the population.
Later, after we learn the central limit theorem,
then we'll talk about x bar, that's the mean of the sample,
and s, that's the standard deviation of the sample.
All right.
Next video, we're going to start by talking
about the uniform distribution, then
we'll move on to the normal and an exponential.
All right.
See you next video.