For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

### Standard Normal Distributions & Z-Scores

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Roadmap
- A Family of Distributions
- Normal Distribution vs. Standard Normal Distribution
- Z-Score, Raw Score, Mean, & SD
- Weird Z-Scores
- Excel
- Types of Problems
- Shape Analogy
- Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer
- Example 2: Heights of Male College Students
- Example 3: Mean and Standard Deviation
- Example 4: Finding Percentage of Values in a Standard Normal Distribution

- Intro 0:00
- Roadmap 0:06
- Roadmap
- A Family of Distributions 0:28
- Infinite Set of Distributions
- Transforming Normal Distributions to 'Standard' Normal Distribution
- Normal Distribution vs. Standard Normal Distribution 2:58
- Normal Distribution vs. Standard Normal Distribution
- Z-Score, Raw Score, Mean, & SD 4:08
- Z-Score, Raw Score, Mean, & SD
- Weird Z-Scores 9:40
- Weird Z-Scores
- Excel 16:45
- For Normal Distributions
- For Standard Normal Distributions
- Excel Example
- Types of Problems 25:18
- Percentage Problem: P(x)
- Raw Score and Z-Score Problems
- Standard Deviation Problems
- Shape Analogy 27:44
- Shape Analogy
- Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer 28:24
- Example 2: Heights of Male College Students 33:15
- Example 3: Mean and Standard Deviation 37:14
- Example 4: Finding Percentage of Values in a Standard Normal Distribution 37:49

### General Statistics Online Course

### Transcription: Standard Normal Distributions & Z-Scores

*Welcome to www.educator.com.*0000

*Now let us talk about standard normal distributions and z scores.*0003

*First we are going to contrast the normal distribution against standard normal distribution.*0008

*It is pretty because just by knowing the normal distribution you already really know the standard normal distribution.*0015

*Then we are going to talk about some normal distribution problems and contrast that with standard normal distribution problems.*0021

*Before we talked about how the normal distribution really is a family of problems, it is not just one shape, *0031

*but it could be stretched or shrunk on that x axis.*0037

*And because of that it is actually an infinite set of distribution with all the different means and different standard deviations.*0042

*You could have means of 10 and deviation of 10.*0051

*That is one way of distribution.*0053

*Another one could have a mean of 1 and a stdev of 2.*0055

*There is like an infinite number of these.*0059

*They all fit the empirical rule.*0062

*Because it is problematic to work with like everything will one of these different normal distribution *0066

*and they have thought of this transformative system where you transform all normal distribution into what is called the standard normal distribution.*0072

*And there are what we are doing is where making that mean 0 and the stdev become 1.*0081

*This way we do not have to worry about the actual values.*0089

*We do not have to worry about the mean of actually 50. *0090

*We just have to know the mean is in the middle.*0095

*And the standard deviation by being 1 makes it really easy for us to label this stuff.*0102

*In a standard normal distribution, what we really done is we have transformed the values into z scores or what we call standard deviation.*0111

*We have normalized everything we do not care that the standard deviation is actually 10.*0133

*We just care how many is the stdev the way they are.*0142

*If you are 1 standard deviation away, 2 standard deviation away, and because of that we have changed this x axis *0146

*instead of actually putting the values we are now putting the z scores.*0152

*That is the only difference between the normal distribution and the standard normal distribution.*0156

*In the standard normal distribution we basically ignore the values and we only use the z scores.*0160

*We have everything in terms of standard deviations.*0168

*Are you 1 standard deviation away, 1/2 standard deviation away?*0171

*That is what we care about.*0175

*In a normal distribution, which I will draw in blue, in a regular normal distribution, we usually have is probability, which is the area.*0180

*This is represented by the area.*0193

*The raw score, with the mean and standard deviations and actual values.*0197

*Things like 150, 450.*0207

*We have the z score, 0, -1, 1.*0212

*That is what we think about a normal distribution, a regular normal distribution.*0220

*What we do in a standard normal deviation is we ignore that part.*0224

*It is the same thing.*0230

*You still have probability and we still have the z scores, right?*0231

*Now all the scores are z scores because we do not have any other scores other than that.*0235

*That is the only thing that is different about a standard normal distribution.*0240

*Now let us talk about the z score, raw score, and the mean, and the stdev, and the relationship that we have to each other.*0250

*Before we really did it in an intuitive way. *0257

*For instance, if our mean was 10, the mean is 10 and our standard deviation is 5.*0262

*How do we know where to draw these notches?*0276

*Well if it is a normal distribution we know that this is approximately this area should be About 68% more than half.*0280

*What you could do is look for the point of inflection and often in my drawings the point of inflections is hard to see *0289

*but in a nicer drawing you could see the point of inflection.*0296

*What we could see is 1 standard deviation away means that it is a distance of 5.*0300

*What would this value be right here?*0309

*Since it is 5 on the negative side, all we have to do is subtract 5 and it is pretty intuitive.*0312

*If we would want to go another five steps to the left and that would be 0.*0318

*If we wanted to go yet another 5 steps to the left that would be -5.*0323

*If we wanted to go yet another 5 steps to the left that would be -10 and so on and so forth.*0328

*Same thing on the positive side, if we wanted to go 5 steps to the right and that would be 15, 20, 25, 30 and so forth. *0335

*On to infinity and negative infinity. Now before we just did it in a very intuitive way and these notches just corresponds with z scores. *0348

*This is 1 standard deviation out, 2 standard deviations out three standard deviations out, *0363

*but there is systematic relationship that we could exploit here in turn with the formula between the z scores, raw score, and mean, and standard deviation.*0373

*If we wanted to go 2 standard deviations out and find what this value was, in order to find the raw score what we do is take the mean *0384

*and then add the z score and multiply by the stdev.*0402

*This actually works with the negative side too because when we have a z score of -1 then you would subtract the stdev instead of adding to the mean.*0408

*This formula ends up being good for us.*0422

*Instead of raw score, we usually call the raw score the axis.*0425

*Instead of writing out mean we would write mule.*0429

*Then we could keep z and write sigma as our stdev.*0436

*Now we see our formula here that allows us to go from the mean, z score and standard deviation into a raw score.*0442

*We could use this formula to find anything, any of those four things.*0452

*If we wanted to find the z score for instance, and we did some algebraic to this *0457

*and we would just see that is actually the distance between the raw score and the mean divided by the standard deviation.*0465

*Let us think for a second about what that means.*0477

*That means the z score is take this distance and cut it open to these chunks.*0481

*How many of those chunks do you have right?*0487

*the z score really *0489

*is telling you how many standard deviations are you away from the mean?*0490

*It is totally relative to the mean and standard deviation. *0495

*Also you can use this very same formula to solve for the mean and standard deviation.*0501

*We could do that over here right.*0509

*Let us say we wanted to solve for the mean, what would that look like?*0513

*All we have to do is move this over so that would be x - z score multiplied by the standard deviation.*0519

*Let us say we wanted to find standard deviation, what would we do then?*0528

*That is pretty easy as well.*0535

*All we have to do is you could just take this formula and swap these guys and that would be stdev = x to find out what is z.*0538

*Here we see that using this very simple formula and you could just remember one of these *0552

*because having one of them, you can derive the other ones from it.*0559

*Just by having one of these formulas if you had any 3 of these you could solve for the fourth one.*0563

*You do not even have to do the algebraic transformations.*0571

*You could just plug them in and find out what is missing. *0574

*So far we have only talked about the z scores for its nice and even like 1, -1, 2, -2.*0583

*We have not talked about weird z scores.*0592

*For instance, what about a z score of something like .5?*0594

*What would be the area over here?*0608

*Some of you maybe tempted to take .34 and divide it in half, but as you will see from this picture that would not work.*0615

*You are not really dividing this area in half, this area still ends up being slightly bigger because it is taller than this area.*0625

*In this area have been chunk out of it.*0634

*You cannot just divide it by half.*0640

*That is not going to be a good strategy.*0642

*That would not give you the right area.*0647

*How do we deal with this?*0650

*Well, there are two ways of dealing with this these weird z scores and how to go from these weird z scores to probabilities that we do not know yet.*0651

*That are not nice than my 34, 13 ½ .*0660

*There are two ways of doing it.*0665

*One way is by looking at up on a table. *0666

*Often there are tables in the back of your text book or even in the back of an EP statistics *0670

*like Princeton Review book or something that show you the transformation from weird z scores like .5 and .67, 1.9 probability. *0675

*That is one way of doing it using z tables.*0690

*The second way of doing it is by using Excel or your calculator.*0694

*If you do not have a fancy TI something calculator, it should also come with similar functions to Excel.*0703

*I’m going to show you those two methods of how to go from weird z scores to probabilities of their z scores and vice versa.*0710

*How to go from the probabilities, like weird probabilities like 50%.*0720

*We do not know where like 51% but we do not know what this value would be for 51%.*0725

*how to go from those weird probabilities into that weird z scores.*0733

*First, let us talk about the method by using the tables in the back of your butt.01225.1 Usually it is the first table you will see back there, table A or something like that and let us break it down.*0739

*A lot of tables looks somewhat like this one here might look slightly different than probably roughly similar.*0752

*And what it shows you up here is exactly what probability is plotted down here. *0760

*What it shows you is the probability that shown certain on the negative side.*0765

*Everything below the z score and this is what we call the cumulative probability because you are accumulating it as we go right.*0771

*It is adding up all the probabilities on this side.*0783

*This is showing you the cumulative probability at the z score.*0786

*The table entry for z is the probabilities lying below z. *0793

*Here the z scores and these are the probabilities.*0801

*Now for the weird z scores, what would really be helpful is if we had z scores of - .34, -.341, -3.42, -3.43.*0804

*We had all of these decimal places.*0827

*It would be really nice if we had all these different z scores.*0829

*That would probably be a skinny list of a whole bunch of z scores and a skinny list of a whole bunch of different probabilities.*0833

*That would be a very inefficient use of space.*0843

*What a lot of tables do is they put the z score up to like here, it is up on the tens place in this side and then we put the hundreds on this dimension.*0847

*In order to find the probability for the z score -3.45, you have to find -3.4 and then go to .05.*0861

*It is like you add this and you stick it on there if you added it would not work because it is negative.*0876

*Here that would be -3.45 and at -3.45 the cumulative probability is .0003.*0887

*Notice that it is a very small probability, it is not 0 but it is very, very small.*0902

*And let us do another example. *0907

*Let us say we wanted to know the probability at the z score -2.48.*0909

*We go to -2.4 and then also go to 8 and that would be our probability .0067 less than -.1%.*0919

*What if we wanted to find out the upper side?*0933

*We are like your only giving me the cumulative probability on the lower side. *0938

*What if we wanted to find out this probability at 2.48?*0943

*What would we do then?*0955

*Because the normal distribution and standard normal distribution to be is perfectly symmetrical *0956

*what we would see is that if we know it for the negative side, we can just flip it over on the positive side.*0965

*The negative side over here at -2.48 is a probability of .00066 then this 2 is also .0066 because it is perfectly symmetrical.*0970

*You do not need to have both the positive and negative sides.*0986

*Oftentimes tables might just give you the positive side or the negative side.*0991

*Sometimes, they will give you both, but you do not actually need both, you could just figure it out from there.*0997

*Let us talk about how to do that with Excel.*1007

*For Excel they are nice functions that Excel prewritten out for us so that we do not have to actually look it up on a table.*1009

*For normal distributions, when you know the mean and the standard deviation, there are ways to go from the raw score to the area underneath the curve.*1018

*So basically it is very similar to that picture we found that z score.*1035

*What it will give you is this cumulative probability.*1040

*That entire area below that value.*1045

*The normal distribution, you need to enter in the mean and the standard deviation.*1050

*In order to go from the score into the probability you would use the normdis function and*1057

*you would put in the score, but you would also put in the mean, the standard deviation.*1066

*and there is another thing, you also have to put in shrew in order to get the cumulative probability because this is sort of asking cumulative probability.*1072

*and that will give you the probability of that score. *1086

*The cumulative probability of that score.*1090

*Norm inverse is just the inverse of that.*1092

*Here we give it the probability and it is been stuck out the score. *1097

*Here you give it the probability, the mean, and the standard deviation, and it spits back out to you the score.*1101

*Notice that these two are inverses that is why one of them is called norm in because in one, you get the probability and the other you get the score. *1112

*These are our 2 flipping around values.*1127

*For standard normal distribution, you do not need to enter in the mean and standard deviation because all standard normal distribution means are 0.*1132

*The mean of 0 the stdev is 1.*1145

*It makes it a lot simpler for us. *1148

*The only difference between a normal distribution and standard normal distribution is this one little letter. *1152

*All you have to do is remember to enter in norm s dis and here you could just put in the score, forget everything else and it will spit out the probability.*1158

*For norm set in, it is exactly the opposite where you put in the probability and a spit back out of the score.*1172

*Another handy little functions might be the functions standardized.*1188

*Here you put in the raw score, the mean, and the standard deviation, and it will give you the z score. *1192

*The standardized function simply uses the formula that we have talked about earlier where *1204

*in order to give you z score, it takes the raw score or x – mule ÷ stdev.*1213

*Given that, let us look at a few examples and do them in Excel.*1226

*The distribution of SAT scores for Math for incoming students to the University was approximately normal. *1230

*That is again important, it has to say approximately normal.*1237

*watch out for that.*1241

*I do not know if you have tricky instructors or tests but sometimes they might give you a problem that looks like a normal distribution problem, *1242

*but it does not say it is normally distributed.*1247

*With the mule of 550 and a standard deviation of 100, what percentage of scores with 400 or below.*1251

*Note that 400 if you transform it into a z score would not it be nice even z score like -1 or -2 is actually like -1.5*1260

*That is going to be a little bit difficult for us to use just the empirical rule.*1276

*That is where we have to use something like either the table in the back of your book or Excel.*1279

*Here I just have an empty Excel sheet and one thing I’m going to do is I’m going to use my columns *1286

*to denote probability raw score z scores just because that can help me keep track of what I’m doing.*1300

*I’m also going to write down my mean and standard deviation just to help make things a little easier.*1308

*550, 100, and my probability where x is less than 400, that is where I’m going for.*1316

*My raw score is 400 and my z score.*1332

*I can just do this in my head it is just the distance 150 ÷ 100.*1344

*It is on the negative side so it is -1.5.*1354

*But just to practice using Excel, let us use our standardized function.*1357

*Excel will guide you into what you exactly need.*1367

*You need your x value for raw score.*1370

*The mean and the standard deviation.*1374

*I’m going to close my parentheses and I will get -1.5.*1379

*The other way you could do this in Excel is do the formula because you know that you need the raw score – mean / stdev.*1384

*You will get the same thing but I just wanted to illustrate for you that is what the standardized function is doing.*1400

*Let us see how that now you need the probability, I could find the probability in 2 ways.*1406

* One, I could use this standard normal distribution or I could use the regular normal distribution.*1418

*Let us do both.*1423

*First, I know that is the norm dist, I do not need the inverse one because I have the raw score, I need the probability.*1425

*Let us start with norm dist.*1434

*Here I know I need my x value and I know I need the mean, stdev.*1437

*I’m just going to ask you it is cumulative?*1445

*Let me just write should.*1448

*That gives us .0668 and that makes sense if we think about where -1.5 was, it is in between -2 and -1.*1451

*If it was at -1, it would be like 16%.*1468

*If it is all the way at -2, it will be like 2%.*1472

*6% sounds like it is in between 2% and 16%.*1476

*We could also do this by using norms set dist.*1483

*For that, all you need is the z score.*1493

*I will put in my z score and I should get the exact same thing because the z score corresponds with the raw score.*1496

*They are right above each other.*1505

*Probabilities at that point should be exactly the same.*1508

*Now let us talk about the different types of problems.*1519

*Now that you know z score and standardized normal distribution, what kinds of problems might come in your way?*1522

*The first sign of information you do not always need these numbers because the first set of information *1529

*is the mean, stdev, probability, raw score or x, the z score or z.*1535

*That is the first set.*1546

*Anyone of these things can be missing and you could find it.*1548

*What is missing here?*1552

*Here we have that same prompt, it says what percentages of scores where 400 and below?*1554

*That is percentages of scores.*1561

*Or it might ask what percent of scores fall below the z score of -1.5.*1563

*Here we see that they are both about percentage of score.*1575

*What might be missing is dist.*1579

*If you have either one of these, and this 2, you could find it no problem.*1582

*Here is another set of problem, same prompt but what is missing here?*1588

*Here it says what math scores separates the lowest 10% than the rest or what z scores separates the lowest 25% from the rest?*1595

*Here you have the probabilities and you have the mean of stdev but one of these 2 things might be missing.*1605

*I think of this as the score missing problems.*1613

*We have probability missing problems and we have score missing problems.*1616

*The last set looks like this.*1621

*Note that this prompt does not give you the stdev but it does give you the z score and the raw score so that you could find the stdev here.*1625

*Or it gives you the percentages and the raw score and then you find the stdev.*1637

*Here something like a stdev is missing.*1645

*You could also find the mean to be missing as well and they would look similar to this problem.*1648

*As long as you have some combination of the other values in place, you could actually figure out what is missing.*1654

*Now let us add in the shape analogy that we did in the previous lesson.*1666

*I’m going to skip over a lot of this because it all stays the same.*1671

*They are only parts where they drive your attention to is right here.*1674

*Before we could only look at our probabilities and raw scores but now we have extended our repeater. *1677

*We could look at probabilities to raw scores to z scores and even find the missing mean and stdev.*1685

*That is all done to a combination of the z scores formula as well as either the tables or Excel.*1693

*Let us do some problems.*1705

*Here is example 1.*1707

*In the US, the distribution of deaths due to heart disease 289 deaths per 100,000 stdev of 54 and cancer a mean of 200 stdev of 31 are roughly normal.*1709

*We know that we could use our normal distribution stuff.*1728

*In California, 254 deaths are form heart disease and 166 deaths are from cancer per 100 residents.*1730

*Which rate is more extreme compared to the rest of the states, the average for the US?*1740

*We have California’s death rate from heart disease and from cancer.*1748

*We want to know which of these are really extreme?*1756

*One way that we could find out is by finding out the z scores.*1759

*I am going to get my Excel out.*1766

*Let us first start with the US.*1777

*The US mean for heart disease. I will use this row for heart disease and this row for cancer.*1780

*The US mean is 289 and the stdev is 54.*1791

*For cancer, it is 231.*1809

*We want to know how extreme the California deaths are.*1813

*It is hard to compare with just the numbers because even though 240 is less than 289, and 166 deaths is less than 200, *1817

*we are wondering how far away from the mean are you?*1833

*One way that we could do that is by using z scores because z scores will give you the distance in terms of the stdev.*1838

*Because these populations have very different standard deviation, that is worth knowing.*1845

*Here is California, heart disease and cancer.*1852

*In California the mean is 240 and 166.*1865

*What we might want to know is the z score.*1875

*What is the z score?*1879

*I might just put standardized and put in my x, put in the theoretical mean that I want to compare it too and my stdev.*1882

*Obviously, I could also do my (x – mean) ÷ stdev.*1897

*Here we see that the z score for heart disease is about 1 stdev away, -.9.*1908

*How far down is cancer?*1918

*How much less is cancer?*1921

*How more healthy are Californian in terms of cancer?*1925

*For here I will put in my regular formula, just so that we practice that too*1929

*My cancer x – theoretical population ÷ stdev.*1935

*I want it in terms of standard deviation step.*1944

*We find out that cancer and this is probably because stdev is smaller and actually sort of out is farther than heart disease.*1947

*The cancer rate is more extreme in a positive way.*1962

*It is more extremely low than heart disease, although they are very close.*1968

*Here the trick is find rates in terms of stdev or z scores.*1977

*Example 2, heights of male college students in the US are approximately normal, estimate the percentage of these males that are at least 6ft tall.*1995

*It will help if we just sketch this out briefly.*2012

*Here is my mean as 70.1, my stdev is 2.7, what percentage of these males are at least 6 ft tall?*2016

*What helps is if you transform this 6ft into inches, that is 72 inches.*2027

*Where is 72 inches?*2043

*That might be something like this.*2045

*What percentage of males are at least 6 ft tall?*2048

*I want all of these people because all of these people are at least 6 ft tall.*2052

*They might be 7 ft tall but they are at least 6 ft tall.*2058

*That is what I really want.*2061

*What might be helpful is instead of my raw score, if I could find my z score and then I can look it up on the table in the book.*2063

*Or I could use Excel.*2072

*I’m going to use Excel to help me.*2075

*Let us find the z score for this.03449.5 In order to find z score, let me write the formula here.*2086

*In order to find my z score for 72 inches that would be 72 which is my (x – mean 70.1) ÷ stdev 2.7.*2095

*Because I want to know how many jumps away, my jumps are 2.7.*2115

*Now I will pull up my Excel and I could just put in (72 – 70.1) ÷ 2.7.*2127

*I find that my z score is .70.*2144

*In order to find the area, the cumulative area, remember cumulative area means this side.*2151

*Excel is going to give me this side but that is now I want.*2159

*I want this side.*2163

*I might put in 1 – this area in order to get that area.*2165

*1 – and will just put in my norms dist.*2172

*Thankfully Excel gives you a little hint if you are a little off.*2190

*What I get is .24, about 24% of these males are at least 6 ft tall.*2195

*This area is about 24%.*2216

*If I want to write it all out I would write my probability where x is greater than 72 inches is .24.*2223

*This is example 3, in a standard normal distribution where P(z score) < .41 = .659, what is the mean and stdev?*2235

*Actually this is a tricky question, before you go often trying to find the z score and all the stuff, note that it says standard normal distribution.*2249

*Every standard normal distribution, mean is 0, stdev 1.*2257

*Example 4, find the percentage of values in a standard normal distribution that fall between -.1.446 and 1.46.*2266

*This is nice if we would sketch this out so that we know what to expect.*2283

*Here is 0, and this is a standard normal distribution that is why I know that it is 0.*2288

*Here is 1, here is where 1.46 is.*2295

*A little bit less than1/2, probably a little bit too much less than half.*2308

*I want to find this area right in between.*2314

*Usually we look at the area between -1 and 1, and we know that 68%.*2328

*We know that it is a little bit more than 68%.*2340

*It is not quite like 95%, it is not quite that high but it is somewhere in between 68 and 95%.*2342

*Let us try to figure this out.*2352

*One way we could do it is by using our Excel or by looking it up in our book.*2354

*In our book and in Excel, our problem is that they will give you the cumulative distribution.*2363

*They will give you this area.*2369

*What we really want is this area.*2372

*What do we do?*2376

*One thing we might want to do is just use our ability to reason so this is 50% of that curve.*2378

*If we take 50% and take away this area, we could use norms dist and put in -1.46 then that should give us this area right here.*2388

*This whole area is this.*2405

*This area is in blue.*2414

*That should give us the red area.*2418

*Here I’m going to put in 50% - norms dist – 1.46.*2421

*I want to take that area and multiply it by 2 because I want the other side too and it is perfectly symmetrical.*2442

*We do not have to do any work just by multiply by 2.*2452

*Then I would get .8557 so a little bit more cloes to 86%.*2455

*That makes sense.*2465

*Since it is more than 68%, it is less than 95% right?*2466

*80 and 86%.*2470

*My answer is where -1.46 my z falls in between this values, .86.*2475

*That is example 4 and that is it for the standard normal distribution.*2496

*Thanks for watching www.educator.com.*2502

0 answers

Post by Ryan Reddell on April 30, 2014

All these questions with no answers. Isn't asking questions answered part of the monthly fee?

0 answers

Post by Marc Patrone on February 18, 2014

In my exam I won't be allowed to use excel or any other program so I would appreciate doing this

the long way. Thanks.

0 answers

Post by Michelle Greene on October 7, 2013

Example 2 HELP! When calculating manually the z-score I do get .7037, however I am not getting .24 from the table. What am I doing wrong? We cannot use excel so calculator or manual way would be be great. thanks.

0 answers

Post by Michelle Greene on October 7, 2013

yes,Please tell us how to solve on the TI 83. On the exams we only have access to our TI83 calculator and not excel.

0 answers

Post by Abdulaziz Baathman on April 2, 2013

4. A normal random variable x has mean Âµ = 1.20 and standard deviation Ïƒ = 0.15. Find the probabilities these x-values:

a) 1.00 < x < 1.10

b) 1.35 < x < 1.50

c) x > 1.38

5. A normal random variable x has mean 35 and standard deviation 10. Find a value of x that has area 0.01 to its right.

pls help me

0 answers

Post by Matthew Compton on February 28, 2013

Is there any helpful links to use for TI calcuators.Since the lectures ignore the needs of your customers that do not use excel.

0 answers

Post by Kristen Gravlee on September 30, 2012

Where is normdist on the calc?

0 answers

Post by Mariya Kossidi on September 26, 2012

teach us on normal calculator, because on the exams students are allowed to have only calculators

0 answers

Post by Kathryn Connor on March 13, 2012

Please show how to do the calculations on a TI-84 calc

1 answer

Last reply by: Kristen Gravlee

Sun Sep 30, 2012 9:36 PM

Post by Kamal Almarzooq on January 22, 2012

you depend on excel too much :(

what about the students who don't have it

teach us how to find it in the normal calculations