A frequently asked question in a college-level Statistics course is, “How do I use my TI-83 Plus graphing calculator to solve probability and statistics problems?” Unfortunately, if you are not used to working with this type of calculator, you will have a hard time understanding the calculations and the function of all those buttons. But, fear not! You can actually do most of the calculations you need to do by using some of the most basic features and get the answers you were looking for.
A word of note here, many times when I hear the above question it turns out that it is not that a student cannot use the calculator, but that they are unsure of how the actual concept works. When this is the case the problem becomes much harder than they need to be and the help of a calculator will not be at all helpful. So please keep in mind that you need to ask yourself a few questions when solving a problem:
1. What I am being asked to solve for?
2. How do I solve for the required quantity? Is there a formula I need to use?
3. If there is a formula, what are the known and unknown quantities in the formula?
4. Do I need to manipulate the formula to find what I am looking for? If so, how do I do that?
5. Did I plug in each quantity correctly?
6. Did I perform my calculations correctly? When using a calculator, did I use the calculator functions correctly?
7. Does the answer make sense? (Note: This is very important, a calculator will only calculate what you tell it to. If you give bad information, you are going to get bad data. This is one of the most common steps students skip and often times answers are wrong because of it.)
Okay, now that I have my calculator usage rant out of the way, thanks for humoring me, let’s discuss how we can we can use the functions of a calculator to solve some problem. As I said above, this is focused on the TI-83 Plus calculator, however the basic functions are available on just about any modern calculator, your task will be to become familiar with those buttons (cough…read the user manual…cough).
Let’s look at an example to determine how we can solve a problem using a TI-83 Plus calculator.
The manager at a shampoo packaging plant determined that there is a 5% chance that a bottle of shampoo is defective. The manager felt that the likelihood of a bottle being defective was independent of any other bottle being defective.
The manager was curious to determine what the probability was that the tenth shampoo bottle in a batch was defective and used a geometric distribution to do so. What would this probability be?
Formula for Geometric Distribution:
Okay, so now we have a question and we need to use the guidelines above to ensure we are solving the problem correctly.
Q1). What is being asked for?
A1). Here we are being asked for the probability that the tenth bottle is defective.
Q2). How do I solve for this?
A2). Notice that we are told the manager used a geometric distribution. Therefore, we know the formula we need to use.
Q3). So what are the knowns and unknowns in this formula?
A3). Here we know p = 5% or p = 0.05 and we know that k = 10, since we are looking for a defect on the tenth bottle. What we do not know is P(X=k) or in other words P(X=10), which represents the probability that a defect occurs on the tenth shampoo bottle.
Q4). Do I need to modify the formula?
A4). Since we are solving for P(X=10) we do not need to do anything with the formula.
Now let’s start working on the formula and try to find a solution.
We know that:
Plugging these values is we get:
Simplifying we get:
Notice I do not show you how to add and subtract on the TI-83 Plus as those should be known to you.
So how do we solve from here using the TI-83 Plus?
There are two paths you can take, each depending on how comfortable you are with the calculator.
Source: Parmanand Jagnandan
Solve each part separately. That is, solve (0.95)9 first and then multiply the result by 0.05. But, how should you enter in the calculator?
Answer: The same way you see it written in. In this case you will use A. the parentheses, B. the caret button, C. the number pad, and D. the ENTER button.
We would enter (0.95)9 as follows in the calculator:
(0.95)^9 and then hit enter.
Then what ever we get we would multiply it by (0.05). Giving a final answer of:
Q5). Did we plug in our values correctly?
Q6). Was the calculation done correctly?
A6). Of course!
Q7). Does the answer make sense?
A7). Yes, we can expect that the probability that only the tenth shampoo bottle was defective should be lower than the probability that any bottle is defective.
This is a quicker path as it requires that we just plug everything in the way we see it in the formula.
In this case we would enter in:
(0.95)^9*(0.05) and then hit ENTER.
The result will be the same value we got before. There is a 3.15% chance that the tenth shampoo bottle will be the first defective bottle.
Source: Parmanand Jagnandan