| Hand in
A. On separate page: Use the "Probability" Applet at http://bcs.whfreeman.com/scc to simulate tossing a penny 25 times. Write down h, the number of heads, and p-hat, the proportion of heads you got (p-hat = h/25). Reset, and repeat, till you have a total of 10 simulations. Make a dotplot (by hand; see D&W p. 36) of your 10 p-hats, using an axis marked with .28, .32, .36, .40, .44, .48, .52, .56, .60, .64 etc. (add numbers at the ends if you need them). Bring your list and dotplot to class to hand in and to share. (Be glad I didn't have you flip a real penny.) ActivStats, Ch.11 HW, ACT 1 and ACT 2: (The disk
in your book is fine for this; you don't need SPSS. ) In Ch. 11("Understanding
Randomness") click on the "house" icon on the top menu bar to get the HomeWork.
Do problems ACT 1 and ACT2, using the "Randomness tool" which opens when
you click on the button in the HW problem.
9 Spinner
Using independence:
Chapter 15, p. 299
Postpone the rest, but it won't hurt to
look at them. I won't spend long in class: Normal
model: Restate each problem using:
"The probability that x is..." ~ ~ "The proportion of the population of
x's that ...." and use your old techniques.
|
Read,
to discuss = = = = = Chapter 14 (uses independence): Read p.283 #25, read answers in back. (a) should have 0.001, not 0.00 for the answer. |
Optional |
(Not explicitly in text)
Continuous sample space: If the sample
space is an interval of values (or the whole line), the possible
outcomes are "x" or "y" values in the interval. The way we assign
probabilities to events is with a density (Day
8). (Remember density curves were idealizations of
histograms--of repeating the "experiment" many many times.)
Area represents proportion-->> Area represents probability.
P(a < x < b) = the probability
that the outcome x is between a and b
is the area under the model's density curve, between a and b.
is the proportion of x's which would come up between a and b
if we did the phenomenon a zillion times.
We declare P(a) = 0 (In a continuous model, getting precisely
a
is utterly unlikely; can't even measure that well),
so P(a < x
< b) = P(a < x < b)
Review ""Tables for simple models (densities)""
HW day 8, restating these parts as
probability questions:
(Copies of the HW handout
are outside my door if you can't find yours.)
Change language from "description of a population of data" or
"area between/above/below" to
"pick an individual at random the population, call the
value x"
A. ("Uniform") Spin the spinner once.
x = number the spinner points to.
a) (example) The probability that the spinner points to a number
less than .6 = P( x < .6) = area to left of .6 = .6.
b) P (.2 < x < .6) = ? Say it
in words: ?
c) For what c is there probability .4 of being greater than
c
?
(In notation: P(x > c) = .4. Find c)
B. y = (number you get from) the sum
of two spinners.
("Triangular")
a) The probability that the sum is a number less than .6 =
P( ?
) =.18
b) P(y > 1.6) = ? P(y < 1.6)
= ? P (y <
1) = ?
P( 1 < y < 1.6) = ? Say each in probability
words.
c) P(c > x) = .08. Find c: ? Say
in words.
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Start here Friday:
Our most important probability model: NORMAL Model family.
Same techniques as before, only we ask "probability that one chosen at
random..." instead of "proportion of all..." Review Normal techniques:
Day
9, Day 10
Take a random sample of size 1 from a population which is
N(110, 25) = =
Give an individual adult, chosen at random, the Wechsler test, which
has a normal distribution, mean 110, s.d. 25. x is her score
on the test.
Find P(100 < x < 145), prob. that the individual chosen
at random gets between 100 and 145. Same as: of all individuals,
fraction who score between 100 and 145. Work is on Day
10, what proportion.
= = = = = = = = = = = = = = = = = =
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