This video will demonstrate a
free online normal distribution calculator
that can be used to determine probabilities.
The URL to the calculator is shown
at the bottom of the screen.
Given a data set is
normally distributed, determine the probability
that a randomly selected data value has a z-score
in the given interval.
Give the answer as a decimal to three decimal places
and a percent to one decimal place.
For part a you're asked
to find the probability the z-score is greater
than negative 0.6.
For a quick review
a z-score, or standard score, is the number
of standard deviations a specific data value is
from the mean of the distribution.
If we plot z-scores on a normal distribution,
it is called the standard normal distribution.
The standard normal distribution is a normal distribution
that always has a population mean of zero
and a population standard deviation of one.
So going back to our examples, again
we will first find the probability the z-score is greater
than a negative 0.6.
Going to the calculator,
at the top we select normal distribution.
Because we are dealing with z-scores,
we know the mean is zero and the standard deviation is one.
Next, to determine the probabilities,
we use these three options.
To determine the inverse probability,
we use these two options.
So we'll be using these three options here on the left
and because we're looking
for the probability the z-score is greater
than negative 0.6, we select the second option
where we have the probability of x being greater
than a particular value, again, because the mean is zero
and the standard deviation is one, this x-value is the same
as the z-score, and therefore we enter negative 0.6.
And then we click Calculate.
The probability is shown here in red, but also looking
at the graph below, you notice the area is shaded
below the curve to the right
of the z-score of negative 0.6 is shaded.
This area represents the probability
which to three decimal places is approximately 0.726.
Let's go ahead and record this.
So we have the probability done to the three decimal places,
which is the percentage is equal to 72.6%.
Next we're asked to find the probability the z-score is less
than negative 1.5.
Going back to the calculator,
we now select the first option
where the inequality symbol is less than, and again because
we have a mean of zero and a standard deviation of one,
we know this is the standard normal distribution
and therefore the x-value is the same as the z-score
and therefore we enter negative 1.5, click Calculate.
Now again, looking at the graph, notice how the area
below the curve to the left of negative 1.5 is shaded.
This area represents the probability, which is shown in red,
to three decimal places, we have approximately 0.067,
which is equal to 6.7%.
And for the third example,
we have the probability the z-score is greater
than negative 1.8 and less than 1.1.
Going back to the calculator one last time,
we now select the third option.
Enter the left-most z-score,
which is negative 1.8, Tab, enter the right-mostest z-score
of 1.1, click Calculate.
Again, notice how the area below the curve,
between the z-scores
of negative 1.8 and 1.1 is shaded.
This area represents the probability the z-score is
between negative 1.8 and 1.1,
which to three decimal places is approximately 0.828,
which is equal to 82.8%.
I hope you found this helpful.