1. Using the TI-84 with Binomial and Normal Distributions
Data Analysis
Tuesday, February 04, 2020

2. The binompdf command
Press 2nd Vars for the DISTRI menu.
Scroll down to A: binompdf(
The syntax for the binomial probability density function command is binompdf(n,p,x).
• n: This is the number of trials
• p: This is the “success” probability. Note that p must be in decimal form.
• x: This is the number of “successes.”

3. Example:
Compute the probability of X successes, using the binomial formula. p is for successes, q is for failures!
(a) n =22, X = 20, p = 0.68
(b) n = 6, X = 0, q = 0.35

4. Compute the probability of X success given n = 12 and p =
Compute the probability of X success given n = 12 and p = .45 using the binomial formula.
P (X>8)
= P(8) + P(9) + P(10) + P(11) + P(12)
Compute the probability of X success given n = 12 and p = .45 using the binomial formula.
(b) P (X< 5)
= P(0) + P(1) + P(2) + P(3) + P(4)

5. A student randomly guesses at 20 multiple choice questions
A student randomly guesses at 20 multiple choice questions. Each question has four possible answers with only one being correct, and each is independent of every other question.
(a) Find the probability that the student guesses EXACTLY 4 correct.
(b) Find the probability of guessing less than 3 correctly.
(c) Find the probability of guessing 18 or more.
(d) Find the probability of guessing between 4 and 6 inclusively.
binompdf(20,.25,4) =
P(0) + P(1) + P(2) =
P(18) + P(19) + P(20) = x =
P(4) + P(5) + P(6) =

6. Example 1 Construct a Probability Distribution
Let X be a random variable that represents the sum when two four-sided dice are rolled. Make a table and a histogram showing the probability distribution for X.

7. Example 1 Construct a Probability Distribution
Let X be a random variable that represents the sum when two four-sided dice are rolled. Make a table and a histogram showing the probability distribution for X.
First you need to enter your data in a list.
Press STAT, choose EDIT. Remember to clear your List!
Enter L1 the X’s and L2 the P(x).

8. How to construct a probability histogram
1. Press 2nd Y= for the STAT PLOT, menu.
Make sure only Plot1 is turned on. Select the histogram plot Type. The
Xlist is L1 (the list containing the x values), and Freq is L2 (the list
containing the P(x) values).
2. If you press #9, you will get an inappropriate plot. (Go ahead and see
what I mean.) We need to set the window variables.
Here
are some guidelines on how to choose the proper settings:
• Xmin: Should always be 0 (the lowest possible value of x)
• Xmax: Start by using one more than the highest possible value of x in
your probability distribution (9, for this example)
• Xscl: Should always be 1
• Ymin: Should always be 0
• Ymax: Pick a value slightly higher than the largest P(x) value in L2 (Use 0.50 for this example)
• Yscl: Sets the spacing for the y-axis tick marks (0.1 is fine for this example)
• Xres: Leave it set to 1
3. Press GRAPH to generate the probability histogram.

9. Example 1 Construct a Probability Distribution
Let X be a random variable that represents the sum when two four-sided dice are rolled. Make a table and a histogram showing the probability distribution for X.

10. Normal Distribution Probability
A Calculus exam is given to 500 students. The scores have a normal distribution with a mean of 78 and a standard deviation of 5. What percent of the students have scores between 82 and 90?
Example:
TI 83/84 directions:
Press [2nd][VARS](DISTR) [2] (normalcdf)
b. Press 82 ,90,78,5)[Enter]
There is a 20.37% probability that a student scored between 82 and 90 on the Calculus exam.
normalcdf(82,90,78,5)

11. 1. Press 2nd and then VARS, this will pick DISTR.
How To: Use the Normal Distribution
Using the TI-84
1. Press 2nd and then VARS, this will pick DISTR.
2. If you are interested in the area under the normal curve with mean μ and standard distribution σ:
a) For, P(a ≤ x ≤ b), select normalcdf(, then enter a, b, μ, σ). Press ENTER.
b) For P(x ≥ a), select normalcdf(, then enter a, 10 ^ 99, μ, σ). Press ENTER.
c) For P(x ≤ b), select normalcdf(, then enter “(-)” 10 ^ 99, b, μ, σ). Press ENTER.

12. Normal Distribution Probability
A Calculus exam is given to 500 students. The scores have a normal distribution with a mean of 78 and a standard deviation of 5. What is the probability students will scores above 70?
Practice:
Normalcdf(70,10^99,78,5)
TI 84
There is a 94.52% probability that a student scored above 70 on the Calculus exam.

13. Normal Distribution Probability
A Calculus exam is given to 500 students. The scores have a normal distribution with a mean of 78 and a standard deviation of 5. What is the probability students will scores below 70?
Practice:
Normalcdf(-10^99,70,78,5)
TI 84
There is a 5.47% probability that a student scored below 70 on the Calculus exam.