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The following are some recommended practical self-assessment questions for the lesson called Better Understanding Continuous Distributions and Stochastic Modeling via the Normal Distribution. They’re intended for you to work through to test your own ability to apply the key concepts we covered there.

A quick note before you start

In the following you will use the function NORMSDIST(). In some versions of Excel this has been made obsolete, meaning you may need to use NORM.S.DIST(). In other versions you may still need to use NORMSDIST(). For our applications, either should yield the same result.

Question 1

In class I gave you two standard normal statistics tables. They were almost the same, but differed slightly in how what ‘area under the curve’ they worked with.

a) Pick your favorite of the two. As discussed in class, I’m giving you two on purpose so you have to choose between them. It’s not rocket science at all. But, I ask this because you’ll need to really understand how such tables work in order to pick one.

b) Make sure you know how to use the one you choose and can answer all of the problems and warm-ups we saw in class. You don’t need to answer those again here as part of your submission. Just make sure you can.

Question 2

a) Build your own version of your preferred standard normal curve in Excel using the =NORMSDIST() function. You might want to check Microsoft’s help page for NORMSDIST() » on this just for clarification of what variables this function takes

In doing this, you might find the guidance in the following video helpful. It doesn’t show the use of the function itself, but it gives some handy hints with respect to ‘absolute referencing’ in Excel and how to use it to set up your table efficiently.

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Welcome (back)!

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b) Write out in full for yourself how the =NORMSDIST() function works, e.g. include what each term means and what it yields, and any other terms you need to add or subtract to make it give you what you need. I know you know this after making the table above, but I’m asking for this because I want you to have it right there in front of you in black and white when you write a quiz or exam.

Question 3

What is the area under the curve corresponding to P(0 < Z < z-score) in the following? Do this with your statistics table, and using =NORMSDIST(). Sketch each situation too.

a) z-score = 3.00

b) z-score = 1.75

c) z-score = 0.955

Notes:

  1. When using =NORMSDIST(), provide the full function you entered into Excel in the written part of your self-assessment submission.
  2. You can use your standard normal table or Excel for these questions. It doesn’t matter to me in a test how you get the numbers. But I’d be using the problems on this page as a chance to make 100% sure you can do both / either at the snap of a finger. By now, you should be looking at problems like this as easy points on a quiz or exam.

Question 4

a) Use the Excel function =NORMSINV() to tell me what is the z-score corresponding to P(-\infty < Z < z-score) = 0.5000. In the written part of your self-assessment submission, provide the full function you entered into Excel. Sketch the situation too.

b) Use the Excel function =NORMSINV() to tell me what is the z-score corresponding to P(z-score < Z < \infty) = 0.0250. In the written part of your self-assessment submission, provide the full function you entered into Excel. Sketch the situation too.

c) Write out in full for yourself exactly how the =NORMSINV() function works to give you the values you want, e.g. include what each term means and what the function yields, and any additional areas you like to add or subtract to get the value you expect. I know you know this after solving the question above, but I’m asking for this because I want you to have it right there in front of you in black and white when you write a quiz or exam.

Note: Microsoft’s help page for NORMSINV() » might help too.

Question 5

Use your table or the Excel function =NORMSINV() to tell me what is the z-score corresponding the following following? Sketch each situation too.

a) P(-\infty < Z < z-score) = 0.5000

b) P(z-score < Z < \infty) = 0.025

c) P(- \infty< Z < z-score) = 0.025

d) P(z-score < Z < \infty) = 0.015

e) P(z-score < Z < \infty) = 0.005

Question 6

Explain for me one last time where the 68.3% rule of thumb comes from for P(\mu-\sigma < Z < \mu+\sigma).

A quick note as you finish

There’s another Excel function called NORMDIST() that can be used in addition to or instead of NORMSDIST(). The first isn’t standardized and the second is, so can be used differently.

They can also be used to yield the same results by standardizing your call to the first function. For example, if z = 1.0 and sigma = 1.0 and mean = 0.0 then NORMDIST(z, mean, sigma, TRUE) = NORMSDIST(z) = 0.84134475.

If you’re one of my students, then you’re expected to answer these on your own and submit them according to the directions provided in class, i.e. you don’t  need to submit them through this website. Don’t forget that our TA and I are both here to help you in the associated lab (and/or tutorial) sessions.

Aim to provide succinct answers to these applications questions in the same document you created for the conceptual self-assessment questions.

I’d also like you to submit an Excel spreadsheet along with that document. This will likely require a bit of thoughtful organization on your part. For example, It would work well to put the answers to both of the above application problems onto their own sheet / tab within your spreadsheet, and name it accordingly. And then you can refer to that specific tab from your written document.

When you answer other applied question sets in future topics, you should do the calculations on separate sheets / tabs, also appropriately named. And refer to them where required to show your work. This way, you’ll have all of your Excel work in one nicely indexed place and will only need to hand in a single spreadsheet as an appendix to each set of self-assessments.

You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.