We'll be working with the Normal model (in addition to the stuff we've been learning) for the next few days...the more fluent you are in working with it, the easier this stuff will be! Check your chapter 6 notes, chapter 6 in your book, or the Normal model section of you Barron's book to review!
Tonight, please complete the worksheet provided in class. You can find the questions below if you lost yours.
- To find the probabilities for this probability model, you will need to find some z scores and either use a z-table or normalcdf!*
- For #1, the answer are: a.) 0.0475; b.) 0.7493; c.) 0.1971; d.) 0.0062
- I didn't teach you how to do 7 yet! Try your best! Take a guess!
Also, I am going to grade this as a homework, not a 16 point classwork...just do your best! I'll provide an answer key tomorrow!
Expected Value, Variance, and the
Normal Model
Suppose that on a
classroom statistics test, the mean test score on the first exam was 75 and the
standard deviation was 6 points. Further, a distribution of these scores proves
to be unimodal and symmetric. Now, let’s suppose your teacher turns your next
test into a sort-of “game show.” That is, he/she will pay you different sums of
money for different scores. We will assume that students’ scores are a random variable and subsequent tests
will reflect the Normal model of the first exam. The payout will break down as
follows:
a. Under
65 points: $0
b. From
65 to 80 points: $50
c. 80
– 90 points: $100
d. Over
90 points: $200
1. Find
the probability that each score falls within the ranges identified above. You
should list your four answers clearly, and show all work in the calculation of
each. (4 points)
2. Using
your answers from (1) above, create a probability distribution for the expected
amount of earnings after the upcoming test. (Your table should include a column
for each outcome ($) and its probability). (2 points)
3. Find
the expected value and variance of your earnings from the test. (Remember
variance is standard deviation, squared!) (2 points)
4. Interpret
your expected value from (3) above in a complete sentence, in context. (2
points)
5. After
a few tests, your teacher is too broke from shelling out cash for students’
good scores. So, to continue this policy, he’ll need to collect some sort of
fee for you to “play.”
a. Based
on your expected value, how much would you be willing to pay to play this sort
of game with your test scores? Explain your reasoning in detail. (2 points)
- If the teacher plans to
quintuple each prize (multiply by 5), find the new expected value and
variance. (2 points)
- Suppose you were going to
play this game three times and add your earnings each time. Find the
expected value and variance for 3 consecutive plays. (2 points)
No comments:
Post a Comment