Math 151 , Sp. '08, Wed., Feb.13, Day 8 .After class. Hit reload..

HW Day7:  Ch. 3: Read Density curves pp. 64-9 .//  Read ahead, please: Normal & 68-95-99.7% rule pp.70-74. Use Normal Density Applet curve to check concepts and computation. "Check" problems p. 84: 3.15, 16, 17, 18;. 19, 20. //Standardizing to standard normal pp.74-76, "Check" 3.21.  Ahead, rest of chapter.  We WILL learn to use table A.   

Hand in  Nothing for Monday but SPSS

Postpone all the rest, but please read the chapter and look at the problems!
A. Complete the Handout on Densities (get from outside my door or link: if you missed class) Solutions
p. 66, 3.1 Sketch density curves
p. 69, 3.2 & 3.3Uniform distribution This is the same density as A on the Handout on Densities.
p. 69 3.4 means and medians
== = = = = = = = = = = = = = 
Normal distribution:  Use the Applet: Normal Density Curve   http://bcs.whfreeman.com/bps4e
(or on your book's CD) to check your answers.
- - - - -Shape related to mean and s.d., 68-95-99.7 rule.  
p. 74 3.5 Women's hts, sketch

p. 74 3.6  Normal, women's hts--68-95-99.7 rule.
p. 74 3.7 pregnancies--68etc rule (This distribution may not apply to planned births, of which we now know there are a lot!)
- - - - - Standardize
p. 76, 3.9 mens & women's heights
p. 86, 3.33 ACT/SAT Jacob and Emily (Info above #3.32)

Read, to discuss

A. Look at table A, pp. 685-6 and compare with the Handout on Densities tables (table A has more numbers; just look at the left 2 columns for now...)  See if you can read from the table that
the area for z less than 0 is .5000,
the area for z less than 1 is .8413,
 the area for z less than -1 is .1587.
 Optional (more practice) 
 
 

= = = = = = = = 
- - - - - - - - - - 
p. 75 3.8  SAT & ACT (Standardize)

First hourly exam, next class  Friday Feb 15 .
Sample exam was handed out Friday.  Problem 7 (density curve) will not be on your exam 1; solutions are linked here,  paper copy to read is outside my door.  Closed book, but bring one sheet of notes (anything you like) and a calculator.
Exam will cover thru what was assigned Friday, Plus reading SPSS output.  You may be asked to read SPSS output (as we see it on the sample exam), but not how to produce it.
You may  start early and/or stay late, if you don't have another class.  You don't have to work in the classroom;  you just have to sign in and say where you'll go (in the building!), on the clipboard.  If you want more than an hour, and have obligations before and after--or other problems-- see or email me to make a plan before Wednesday! 
Questions on HW Day6?   (standard deviation)  None. Review Std. Dev. Day 5
Questions on SPSS? Day 6   Where  have people used it successfully? Main, others. Files for textbook problems are on your CD! See SPSS Info page for details.
 Solutions for SPSS HW problems is posted in Mac 101, 110, linked here.. (Mac 101 is going to be closed a lot.)
Questions for the exam?
Thank you for all the excellent questions today. Sorry about the software glitches!
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We started this but didn't get very far. Will pick up here Monday, cover this page and maybe more!
Density curves, BPS4e pp.64-69
GET  handout HW sheet: "Density curves" if you didn't
See Day 6 for notes & handout link.  Outline:

Any density curve:  is a curve --always on or above the horizontal axis    --has area exactly 1 underneath it.
 This allows area to represent proportion of "histogram" between specified values.
Median, mean, percentiles, standard deviation are defined for a density curve in analogy to those for a histogram.

Many densities have tables to describe them.  Especially tables showing area to the left of (below) a given value ("Cumulative Proportion").

  • You will make and use  "Cumulative Proportion" tables for the simple distributions on the handout.  These are similar to the table we will use to describe the normal distribution.
    • Maybe? Some?:
    "Normal" distributions:("Gaussian", "Bell-shaped") part 1 (pp. 70-74) 
    Applet: Normal Density Curve       http://bcs.whfreeman.com/bps4e Example:  "Classic IQ test" scores are approximately N(110, 25).  mean=110, mean +1s.d. = 135, mean + 2s.d.'s = 160,  mean -1s.d. = 95, etc.  See picture below.

    Standardizing: (p. 74-5) A "raw value" x is standardized by telling how many standard deviations above the mean it is.
        Find z:  Subtract the mean from x.  Now you know how far "above" the mean x is, in "raw" units. (If it's below the mean, the number will be negative.)  Find how far this is in "standard deviations" by dividing by the standard deviation.
    That's the z-score.
    Values in any normal distribution, after standardizing, become values in a N(0,1) "standard normal" ("Z") distribution.

    Standardizing:   A way of comparing an individual against its pack.
                                    Comparing individuals from different packs, each relative to its own.
                            Removes "units of measurement" from the discussion.
                            Enables use of the standard normal table.

    Examples: "Classic IQ test" scores are approximately N(110, 25)
       A score of   85 is 1 s.d. below the mean.  Computation:  z = (85 – 110)/25 = (–25 raw points)/25 = –1 s.d. from mean.
               (About the 16th percentile--16% get scores < 85)
       145 is how many s.d.'s above the mean?
                Computation: z = (145 – 110)/ 25=  (35 raw points above mean)/25 = 1 2/5 = 1.4 s.d. above mean
               (What percentile is this?  What percent get scores < 145?  Need a table for between the "whole" s.d.'s.  Next.  Table A)

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