Did you read my tips on how to study and learn Stat 2000?  If not, here is a link to those important suggestions:

Did you read my Calculator Tips?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 1?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 2?  If not, here is a link to those important suggestions:

Study Lesson 6: Discrete Probability Distributions in my book (if you have it) to prepare for this assignment.  You also need to study the Probability handouts I provided earlier.  Here is a link to those handouts:

Note that the upcoming midterm only covers the concepts in the first three questions of this assignment.  I suggest you only study the Probability Handouts and the first three questions of my Lesson 6 at this time.  Study the rest of Lesson 6 and complete the assignment after your midterm exam.

Don't have my book?  You can download a free sample containing Lesson 3 at my website here:

It appears that StatsPortal is not fully functional if you are using Internet Explorer as your browser.  This has ramifications if you are using the HTML Editor box.  I strongly recommend that you use Mozilla Firefox as your internet browser whether you use a Mac or PC to ensure no problems with submitting your assignments.  Here is a link where you can download Firefox direct from Mozilla (it is free):

Do note that every time you exit a question in StatsPortal, the next time you return to it, the data may very well change.  Do not press the "back-up" button on your browser in a question.  That, too, will change the data.  When you are prepared to actually do a question, open the link, keep it open, and do not close it until you have submitted your answers.  There is also some debate whether even pressing "Save Answers" locks the data in place.

You should also have already downloaded the JMP statistical software which was provided with either one of the course options for StatsPortal as mentioned in your course outline.

Make sure you have gone through Assignment 0 completely to learn how to use the interface.  I also suggest you print out a copy of question 8 in Assignment 0 (Long Answer Questions - Part 3) so that you have the steps for saving and uploading files into the HTML editor in front of you.

Don't forget to click the Html Editor link before you type your answers into their box.

I show you how to determine a Sample Space through the use of two-way tables if necessary in  Probability Handout above.  Note that all you are asked for is the sample space in each part, so your answer would be something like this (don't forget to use those squiggly brackets "{}"):

For example, here is the sample space for the outcome of flipping a coin twice where H=heads and T=tails:  {HH, HT, TH, HH}.

For part (c) note that your outcomes are not all the same size since you quit selecting the moment you pick C, a cherry.  For example, you would never have the outcome CG because, once you picked C first you would quit picking candies.  Outcomes will therefore always end with C, such as C or GC or GLC.  There are others.

This is a question best solved by Venn Diagrams.  Make sure you have studied that section in my Probability Handout above of my book and have done questions 14 to 18 before you attempt this question.  Make sure you have definitely looked over my examples of how to prove two events are independent or not in those questions (as well as others earlier in the lesson). 

This question is very similar to my question 18.  However, they do not give you enough information to fill in every part of your three-circle Venn diagram.  Similar to what I do in my question 17, you will need to put x in one of the missing parts of your three-circle diagram, then solve for x.

Don't enter percentages into your Venn, use decimals to set up for the format StatsPortal wants for your answers.  For example, if the percentage is 32.15%, enter that as 0.3215 in your Venn.

You are given the percentage that follow all three sports, so you can put that value in the centre of your three-circle diagram.  You are given the percentage that are SK and SS fans, so you can fill the appropriate region in such that the two regions representing SK and SS add up to this given percentage.  You are also given the percentage that are SK and SB fans.  Again, there are two regions in the diagram representing that, and you already know the number in one of them, so you can fill in the missing part knowing the total must be this SK and SB amount.

Here is where things get tough.  You are not given SB and SS, so put x in that region that you are missing.

Now, we go to the first piece of info.  We are told the percentage that are SK fans.  There are four regions in the SK circle in your diagram, and you should have numbers already in three of them, so you can figure out what value to put in that fourth region to make the total correct.

We are also given the percentage that are SB fans.  The problem is that we have four regions in the SB circle but only have two numbers filled in.  First add those two numbers and subtract from the total SB percentage.  For example, if you have 70% that are SB fans, and the two given regions add up to 30%, that leaves 70-30=40% to put in the remaining two regions.  One of those regions is already labelled x, so that means the remaining region can be labeled 0.40-x.  Of course, these are not your numbers.

We are also given the percentage that are SK or SS fans.  There are six regions in your diagram that represent SK or SS.  You already have numbers labeled in four of them (the four in the SK circle).  Add those four up and subtract them from the SK or SS amount to see what is remaining.  For example, if you know 40% follow SK , and 52% follow SK or SS then we know that 52-40=12% remains to put in the two remaining regions of the SS circle.  One of those regions we have already labeled x so we will label the other region 0.12-x.  Again, these are not your numbers, of course.

Finally, we are given the percentage that are SB or SS followers.  Add those six regions up.  You will note that, besides the numbers, you will be adding -x + x + (-x).  This collects up to just -x.  Of course, there are also a bunch of numbers you can add up in those six regions, so, if all the numbers add up to say 62%, then we discover the six regions add up to 0.62-x.  But we can set that equal to the percentage that do follow SB or SS and solve x.

Once you have solved x, you are rolling. 

Don't even think about asking me any more questions about this one.  I have told you too much as it is.  You are on your own from there.

Note, in part (a), when they ask how many outcomes there are, count every single region in your Venn diagram to count all the possible outcomes.  For example, a classic two-circle Venn diagram like my question 16, has four separate regions (four separate probabilities or percentages are labelled in the diagram).  Therefore, question 16 has 4 outcomes in its sample space.

This question is a good runthrough of two-way tables and probability distributions. Be sure that you have gone through all of my questions 3 to 13 in the Probability Handout before attempting this question. My questions 4 and 13 are especially similar to this problem.

Parts (d) and (e) use the formulas for mean and variance I introduce in question 1 of my handout, or also use in Lesson 6, questions 1, 2 and 3.

You have two normal distributions, X and Y.  You can use the properties of mean and variance I teach at the start of Lesson 4 to work out the mean and variance of X + X.  Since X and Y are both normal distributions, X + Y is also normal.  You can also compute the mean and variance for X - Y.  You also know that X - Y is normal.

Of course, to change your score into a z-score, you will have to use the standardizing formula you first learned in Stat 1000, z = (x - mu)/sigma or z = (x - μ)/σ.

Part (a) wants X < Y.  Rewrite that as X - Y <  0.  Similar things can be done for the other parts.

Lesson 6.  If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:

1. There must be a fixed number of trials, n.
2. Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.
3. Each trial must be independent.
4. X, the number of successes, is a discrete random variable where X = 0, 1, 2, ... n.

Hints: If you are reading off numbers from a randomly selected row in the random number table, note that every row has 40 digits.  That is like 40 trials looking for whatever digit you may be looking for.  What is the probability that, at any moment on the table, the next digit is a 0, or a 1, or a 2, etc..

If you are selecting objects, are you sampling with replacement (independent trials) or without replacement (dependent trials)?

I introduce the formula for mean and standard deviation of a binomial distribution in my Lesson 6, question 10.  Be careful that you are using the correct n and p for each question since they keep switching which flight and how many years and flights they are talking about.  Note that n is the total number of flights he has taken to a specific destination during the time period, not just the number that arrive on time.

I teach this  in Lesson 6 in the "Hypothesis Testing Revisited" section.  Note that you can use Table C to solve the probabilities more quickly.  My question 19 is very similar.

Standard Poisson stuff as taught in Lesson 6.  Make sure you are using the correct value for lambda.

Standard Poisson stuff as taught in Lesson 6.  Make sure you are using the correct value for lambda.

You're on your own for this one.