Math 151 , Fall 2005, Day 26 Wed. Oct. 26 Hit reload  After Class

Exams not finished.  Sorry!
Day 26 (Wed. Oct. 26): Reading: Continue D&V Part IV: Ch.15 thru p.  291 (then Ch. 18 &on. ) ActivStats is very good for part IV--Ch11"Randomness" shows Law of Large Numbers as D&V express it. Ch14, 15"Intuitive Probability"&"Probability Rules" correspond well with the text and present very good examples.
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. 
1 Roulette
Winter
Crash

9   Spinner
11 a Car repairs
13 a M&M's

Using independence: 
11 b Car repairs
13 b M&M's
19 Champion bowler
15 Disjoint or indep?  Read p.290 top, with this. 

Chapter 15, p. 299
1 Sample spaces
Continuous sample spaces: 
Do the questions A and B in webpage below, with the Tables for simple models (densities) handout

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. 
p. 352 #21 a, b only. Pregnancy Find the solutions, then Restate a and b from proportion questions to probability questions:  "What is the probability that a pregnancy chosen at random will last... ... " and "If the chances of a random pregnancy lasting longer than k days is.... ..., then what is k?" 
p. 265 #28a only Rivets
p. 353 #33a only IQ's,  #34a only Milk

Read,
  to 
discuss 
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Chapter 14 
(uses independence): Read p.283 #25, 
read answers in back. (a) should have 0.001, not 0.00 for the answer.
Optional 
Randomness and Probability (Notes on Days 23 and 24)  Day 23,      Day 24

(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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there will be none or only one from  0, 1, 5, 9.  At least one and probably more 7's. A"bias" against 0,1,5,9, and toward 7.