Stat 1000: Assignment 7 Tips (Distance/Online Sections)
Published: Tue, 10/16/12
My tips for Assignment 7 are coming below, but first a couple of announcements.
Please note that my second midterm exam prep seminar for
Stat 1000 will be on Sunday, Nov. 4, in room 100 St. Paul's College,
from 9 am to 9 pm . For complete info about the seminar, and to register if you have not done so already, click this link:
I am also offering seminars in Calculus, Linear Algebra, and Stat
2000 in the coming weeks. You can get info about those seminars here:
Make sure you have read my Tips on How to Do Well in this Course
Did you miss my Tips on what kind of calculator you should get? Click here
If you are taking the course by Classroom Lecture (Sections A01, A02, etc.), click here for my tips for your Assignment 2.
Tips for Assignment 7 (Distance/Online Sections D01, D02, D03, etc.)
Study Lesson 5: Introduction to Probability in Volume 2 of my book, if you have it, to prepare for this assignment.
Question 1:
When you are asked to
list sample spaces, generally you will use a two-way table to visualise
all the possible outcomes. If you are asked to count the number of
things (number of coins, number of successes, etc.), list the sample
space from lowest possible number up. Don't forget that, when counting
the possible number of things, there is always the chance that there
could be 0 things. In those cases, the sample space might be something like {0,1,2,3}.
Some of you are asked to list sample spaces that are huge or endless in size, so they say, "list enough to make it clear." For example, if you were asked to list the number of students in a classroom who use Facebook, there might be 0 students who use it, 1 student, 2 students, etc. We don't know how high the number might be because we don't even know how many students are in the class, so we would say the sample space is {0,1,2,3,...}
Some of you are asked about coins. Note, they are
not asking you what denomination the coins are (pennies, nickels, dimes,
etc.). That is irrelevant. They don't care what kind of coins you
might have, just how many and how much money are they worth.
When they ask
you, "Are the outcomes equally likely?", think carefully. Remember, to
be equally likely means that the first outcome you have listed in your
sample space, has the same probability of happening as the second
outcome, etc. Don't think that because the outcomes are equally easy to
list, that makes them equally likely.
For example, if I ask you to the list the sample
space for the possible medals an Olympic athlete might win, I could say
the sample space is {Gold, Silver, Bronze, No medal at all}. Even
though there are four possible outcomes, they are not equally likely!
There is not a 25% chance of winning a Gold medal, for example. It
depends what athlete we are talking about, what event, etc. The mere
fact I have to say "it depends" tells me the outcomes are not equally
likely. Even if the actual medal someone won was randomly determined
and we were assuming every person has an equal chance of winning, if
there were 20 people competing for the medal, there would be only a 1/20
chance they would win gold (since only one person can win gold), and a
17/20 chance they win no medal at all. Of course, some athletes may be
the favourite to win gold and they would then have a much higher chance
than 1/20 of winning.
Of course, some outcomes are equally
likely. For example, if you are flipping a fair coin, or rolling a
fair die, you have every right to say either side of the coin or die are
equally likely to come up.
Be careful! Let's say you were listing whether or not a baseball team Wins or Loses in each of its next three games. Even though that means each outcome is either Win or Lose, don't you dare say that makes them 50/50! Whether a team wins or loses depends on how talented the team is (and how talented their competition is). If they are really good team, they may have a very high probability of winning. If they are a really bad team, they may have a really low probability of winning. If Win/Lose depends on the quality of the team, that means you can't say it is 50/50. It is not equally likely.
Question 2
I think they are quite clear what to do in this question which
has you read digits off of Table B.
Look carefully at their example for reading Line 101. You look at the
first five digits (19223) and record the highest digit you saw (9); look
at the next five digits (95034) and record the highest digit (9);
05756, the highest is 6; 28713, the highest is 8; etc. You have to do
this a total of 50 times. How many times did you record a 9? How many
times did you record an 8? A 7? A 6? etc.
When making your stemplot,
consider all the 9s as 09s, all the 8s as 08s, all the 7s as 07s, etc. The stemplot might look something like this:
Stem | Leaf
0 | 555
0 | 6666
0 | 77777777
0 | 8888888888
0 | 99999999999999999999999999
Trust me, whatever the shape of the distribution of your
sample is, that is also likely to be the shape of the population if you
had done this an endless amount of times. Ask yourself, will you get 0
the same number of times as you get 9, if you do this over and over
again? Will 1 be as common a result as 8?
Question 3
This question combines the fundamental concepts of a discrete distribution I illustrate in question 1 with some two-way table stuff not-unlike my question 6.
Question 4
This question is similar to my question 4 except they have been nice enough to list all the outcomes for you, so you don't need to make a two-way table. Could you have come up with this sample space yourself? Note, in part (c), you need to realize that, as long as any of the shear rams work, a blow-out will be prevented. You don't need all of them to work (although that would be fine too). This is the usual thing that is done for vital machinery, like important parts in satellites or something. Built-in redundancies, where, if one part fails, there is a back-up that can takeover. Because, you can't risk the machine stopping work altogether. You can't send a repairman up to a satellite everytime a part fails. It has to have back-ups ready to takeover.
Question 5 is dealing with a density curve.
Be sure to review the first two questions in Lesson 4: Density Curves and the Normal Distribution of my book
(Lesson 2 if you have an older edition) to better understand what is
going on here. Simply shade the relevant region on the graph and compute the area. You will need to use the area of a rectangle (length * height), or perhaps add together areas of more than one rectangle.
Question 6 is more probability practise. Different students get different questions relating to the concepts I teach in Lesson 5.