Stat 1000: Tips for Assignment 7
Published: Thu, 10/20/11
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Study Lesson 5 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 visualize
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. 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.
I think they are quite clear what to do in question 2 which
has you read digits off of Table B (Remember that I gave you a link to download Table B in the previous assignment tips). When making your stemplot,
consider all the 0s as 00s, all the 1s as 01s, all the 2s as 02s, etc.
Then, as they say, you will have a 0 stem where you list all the 0
leaves, a 0 stem where you list all the 1 leaves, 0 stem where you list
all the 2 leaves, etc. Trust the graph you make.
Questions 3 and 4 are quite similar to my questions in Lesson 5.
Question 5 is dealing with a density curve. Be sure to review the first two questions in Lesson 4 of my book (Lesson 2 if you have an older edition) to better understand what is going on here.
Question 6 is just more probability practise.