Tomorrow in class we'll do some practice AP problems (in groups); then, on Monday we'll have our chapter 16 vocab quiz and do some more chapter 16 to wrap up! See you there!
Here's the homework in case you lost yours or were out:
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
60 points: $0
b. From
60 to 80 points: $50
c. 80
– 90 points: $100
d. Over
90 points: $200
1. Find
the probability that each score falls within the ranges identified above.
(Hint: when we need probabilities or proportions under a Normal curve, where do
we have to look?) You should list your four answers clearly, and show all work
in the calculation of each. (4 points)
2. Using
your answers from (1) above, create a probability distribution for the expected
amount of earnings after the upcoming test. (Your table should include a column
for each outcome ($) 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)
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