My Midterm Exam Prep Seminar for Stat 1000 is Saturday, November 1.  It is NOT on campus.  It is held at Canadian Mennonite University, on the SOUTH side of Grant Ave., at 600 Shaftesbury Blvd.  In the Lecture Hall.  It costs $20 if you bring my book to the seminar, or $40 without a book. 

Did you see my tips for Assignment 1? Click here.

Did you see my tips for Assignment 2? Click here.

This question is very similar to my question 2 in Lesson 4.

In part (d) you will have to work backwards.  Arbitrarily mark b as some random value on your horizontal axis.  Then mark the given right endpoint further along on the right axis.  Shade the region between b and the given right endpoint.  That rectangular shaded area is what they are describing.  You are given the proportion which tells you the area of the shaded region.  You also know the height of the shaded region (your answer from part (a)).  So, you can establish what the width of the shaded region must be because you know the width times the height equals the area.  Then, you can establish what b must be knowing that Right - Left gives you the width.

I strongly recommend you read my section in Lesson 4 about the Z Bell Curve Ladder and the X Bell Curve Ladder and make the ladder every single time you have a bell curve problem.  Then climb up or down the rungs.  Many students are guilty of not thinking a problem through, and consequently looking at Table A too soon.  The ladder trains you to focus on the fact that Table A deals with z scores and Left Areas, but your problem may be interested in something else.

You will be using Table A for much of this assignment.  Here is a link where you can download the table if you have not already done so:

This is very similar to my Lesson 4, question 5.

This is very similar to my Lesson 4, question 6.  For part (a), note that I also do a percentile example in my question 7.  As I say in my question 7, the 80th percentile, for example, is the z score that has 80% of the area to the left of that score.

Make sure you have studied all my X-Bell Curve problems (questions 9 to the end) in Lesson 4 before you attempt this question.  Make sure you use the X-Bell Curve Ladder to help you work your way through each part of this question.

You also need to know the 68-95-99.7 Rule taught earlier in my lesson (questions 3 and 4 in Lesson 4).  But, only use this rule to solve part (e).  Never use the 68-95-99.7 rule unless you are clearly told to do so!

Part (h) is all about z scores.  The higher your z score in a normal distribution, the better you did relative to others.  See my question 14 in Lesson 4 for an example of this principle.

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 Lesson 5 of my book.  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}.

Don't state the probabilities!  You are not asked for the probabilities.  In fact, in many of the situations students will be given for this problem, it is impossible to know the probabilities.  You are just asked for the sample space.

With cards, focus on what you are asked to select.  You don't have to list all 52 cards.  Is it just the colour of the card you are interested in (Red or Black?, R or B). Is it the suit of the cards (C, D, H, S)?

In part (c), note that there are only three coins, one of each for G, S and C, and you are sampling without replacement until you get G.  So, if your first selection is G, you stop.  But, if you get S or C, you proceed to make another selection.  Your sample space will look something like this:

{G, SG, CG, ...}

This is a question best solved by Venn Diagrams.  Make sure you have studied that section in Lesson 5 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.

Start with the last piece of information they give you.  You are given the percentage who follow all three teams, so you can put that value in the centre of your three-circle diagram. 

Now climb up your givens.  You are given the percentage that are J and G fans, so you can fill the appropriate region in such that the two regions representing J and G add up to this given percentage.  You are also given the percentage that are J and B 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 J and B amount.

Here is where things get tough.  You are not given B and G, 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 J fans.  There are four regions in the J 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 B fans.  The problem is that we have four regions in the B circle but only have two numbers filled in.  First add those two numbers and subtract from the total B 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 J or G fans.  There are six regions in your diagram that represent J or G.  You already have numbers labeled in four of them (the four in the J circle).  Add those four up and subtract them from the J or G amount to see what is remaining.  For example, if you know 40% follow J, and 52% follow J or G then we know that 52-40=12% remains to put in the two remaining regions of the G 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 B or G 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 B or G 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 example of a 2-way table problem.  It is sort of a combination of my Lesson 5, questions 4, 5 and 6.

In part (b), you are asked for first green OR second red.  NOT AND!

I think it is a good idea to use my "check-mark method" that I show you in my Venn diagrams section when dealing with AND or OR.  In your sample space, check off all the outcomes that belong to A.  Now go back and check off all the outcomes that belong to B.  This might mean you are checking off the same outcome twice.