Math 151 , Day 23, Wednesday, Oct. 24, 2001 final version

Exam on Friday: Sec. 2.3 through last HW.
Closed book, notes.  I'll supply any tables needed (Random numbers) More details

Handout (current events) FYI -- Census will not sample.
QUESTIONS on Exam material, HW?

Random variables with intervals of outcomes ("continuous") Sec. 4.2 pp. 228-232
If the sample space is an interval of values (or the whole line), the way we assign probabilities to events is with a density curve (cf. Sec. 1.3, Day 7) (remember density curves were idealizations of histograms--of repeating the "experiment" many many times)
  P(a <  X < b) = the probability that X is between a and b  is the area under the density curve, between a and b.
We declare P (X = a) = 0 , so P(a <  X < b) = P(a < X < b)

Answer the following for Homework for Monday (fill in the ? spots)
Review "Density curves" HW day 7, 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" to "pick an individual from the population, call the value X"
A. ("Uniform") X = number the spinner points to.
a) (example)  The probability that the spinner points to a number less than .6 = P( X < .6) = .6 .
b) P (.2 < X < .6) = ?   Say it in words: ?
c) For what x is there probability .4 of being greater than x ?      (In notation: P(X > x) = .4.  Find x)

B.  Y = (number you get from) the sum of two spinners.
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) =  ?
c)  P(Y > x) = .08.  Find x:  ?

Our most important probability model is the NORMAL DISTRIBUTION family.  You use the same techniques as before, only we ask "probability that one..." instead of "proportion of all..."

Monday we'll consider the Next question: We take a simple random sample of size n, find the sample mean xbar.  It will be different depending on the sample, so we have a random phenomenon.  We measure the outcome as a number, the sample mean, so we have a random variable Xbar.
What probability distribution describes the random phenomenon of finding xbar from a SRS?
That is, what is the distribution of the random variable Xbar, when the experiment is to take a simple random sample of size n? We'll call it the "sampling distribution of the sample mean" (Sec. 4.3)

HW Day 23, Wednesday, Oct 24  Prepare for exam Friday. Good luck!
This HW finishes 4.2.  Monday we will discuss these and continue with 4.3.  (Skip 4.4 and Skip Ch. 5).
Hand in Monday: 
Rest of sec. 4.2--Sample space is an interval of outcomes, not a finite list. (pp. 228-231) 
Do the questions given above
p. 229 4.22 uniform, 0-1 (Note, this is distribution A above)
  4.23 sum of two uniform (Note, this is distribution B above)
p. 236 4.37  uniform on 0-2 (This corresponds to a spinner with its edge labeled with values going from 0 to 2, rather than the 0 to 1 we used in our homework up to now.)
p. 231 4.24 normal
p. 249 4.51 part a.   cola fill

sec. 4.3  Sampling dist. of the sample mean:
p. 241, 4.40 do a and b; Do b this way.  Close your eyes and put your finger down somewhere on table B.  Start reading the table where your fingertip lands. 
Repeat part b, to get a total of 3 values of xbar. (You can just keep reading the table where you left off, or you can put your finger in a different spot).  Make a dotplot of your 3 values and bring the values to class to be compiled with everyone else's.		 Read, to discuss 


 
 
 
 
 
 
 
 

 

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