Welcome to lesson on how to use the TI-84 graphing calculator
to find the probability of a data value being
below and above a given Z-score
in a normal distribution. And also how to find the probability
of data value being between two Z-scores
of a normal distribution. So for our first example,
we want to find the probability of a randomly selected data value
from a normal distribution having a Z-score below one point four.
Meaning the probability that Z is less than one point four,
and the probability that the Z-score would be
above one point four, given here is a probability of Z
greater than one point four. Remember if Z equals one point four,
the data value would be one point four standard deviations
above the mean. So this is the standard normal distribution
let's say Z equals one point four is somewhere in here.
The area to the left
would represent the probability that Z is
less than one point four. And the area to the right
would be the probability that Z is greater than one point four.
And the area would represent the probabilities that we're looking for.
So instead of using the Z-score table,
we can use the TI-84 graphing calculator to determine these probabilities.
Where if we use the normal CDF feature,
then enter A, comma, B, comma, mu, comma, sigma.
This gives the values of the cumulative normal density function
occurring between X equals A, and X equals
B. This would be the cumulative area under the standard normal distribution.
But in our case, if mu and sigma are not specified,
then mu equals zero and sigma equals one,
and therefore, A and B would be the lower bound an upper bound
Z-scores. So because we already have the Z-score,
we will leave off mu, the mean and sigma,
the standard deviation. But notice how we do have to have a lower and upper bound
Z-score.
One point four would be the upper bound the Z-score.
For the lower bound, we'll have to make this up. We know if Z was equal to negative three,
that would be almost all the entire data, so we'll exaggerate the lower bound
Z-score
and use something very, very small. So to begin,
we'll press second, vars for distribution.
Option two for normal CDF.
We'll first enter our exaggerated lower bound Z-score.
Let's use negative ninety-nine thousand, nine hundred ninety-nine,
comma, the upper bound Z-score which we know is one point four,
closed parenthesis and enter.
This gives us the cumulative area to the left
where Z is less than one point four. So to four decimal places,
the probability that Z is less than one point four
would be approximately zero point nine, one,
nine, two.
And therefore, the probability that Z is greater than one point four
would be one minus zero point nine, one, nine, two,
or zero point zero,
eight, zero, eight.
Let's take a look at the second example.
Here we want to find the probability of a randomly selected data value from a
normal distribution
having a Z-score between zero point five,
and two point one, which we can express in this way here.
So if this is the standard normal distribution,
the lower bound Z-score would be
negative zero point five, let's just say somewhere in here.
The upper bound Z-score
would be Z equals two point one, let's just say somewhere in here.
So this probability would be equal to the area
bounded by these two Z-scores. And we can quickly determine this area
which would be our probability using the TI-84.
Again we'll press second, var's for distribution,
option two. And now we'll enter the
two Z-scores. The lower bounds Z-score is
negative zero point five, comma.
The upper bound Z-score is two point one. And again, because we have the Z-scores,
we're leaving off mu and sigma, so we need a closed parenthesis
and enter. The probability that Z is
between negative zero point five and two point one
is approximately zero point six, seven,
three, six.
I hope you found this helpful.