Math 151 , Spring '12, Mon. Feb. 13, Day 10.After class. Hit reload..

Reading :  Ch. 3: Normal pp. 73-74, & 68-95-99.7% rule pp.74-77. Use Normal Density Applet curve to check concepts and computation. "Check" problems p. 87: 3.15, 16, 17, 18;... 19, 20. //Standardizing to standard normal pp.77-79 "Check" 3.21. Ahead, rest of chapter.  We WILL learn to use table A. Moore doesn't separate out reading the z-table in the following; focus on just the z-table parts on first reading:  p. 79-83, Cum. proportion and  normal.  "Check" 3.22, 3. 23. "Backward" from prop. to z pp. 83-86.  We'll revisit and learn to deal with x's.   

Hand in Wednesday
Remaining SPSS!  All due Wed.  Day 6

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Normal distribution:  Use the Applet: Normal Density Curve  to check your answers http://bcs.whfreeman.com/bps5e (or on your book's CD).  These Normal templates, (optional)(bell shapes) may help you with drawing and labeling and proportions (you can "count squares" like the Density handout.)

- - Shape related to mean and s.d., 68-95-99.7 rule.  
A. Sketch a normal curve with mean 5, standard deviation 10, and label the horizontal axis correctly. Use the applet to check your work, and for help with labeling the horizontal axis.

p. 77 3.5 Running a mile, sketch Use the applet to check your work, and for help with labeling the horizontal axis.

p. 77 3.6  Normal, Running a mile--68-95-99.7 rule.
p. 77 3.7 Monsoon rains
p. 88, 3.26 Daily activity (obese/not) This is based on the same study as you saw before.
 ...

- - - Standardize
p. 79, 3.9 mens & women's heights
p. 79, 3.8 ACT/SAT Eleanor and Gerald
~ ~ ~ ~ ~ ~ ~
: Sketch and label the Normal curve, mark the axis, shade the desired region, get pretty good answers from the Applet.  Leave room for the table-computed answers...~ ~ ~ ~ ~
- Using table with "z"'s--standard normal.--
Table use--z: Always sketch a normal curve first, mark the area you are looking for!  Do these with Table A, and check your answers with Applet: Normal Density Curve on your CD or at    http://bcs.whfreeman.com/bps5e. (Uncheck the 2-tail box for most uses. Mean 0, s.d. 1)  Your answers may differ in the second decimal place because the Applet only goes by .02's on the z-axis --.64, .66, .68... and Table A goes by .01's.
  p.83 3.10  z's to proportions, using Table A.

- Postpone backward z: (but Start the YES problems below!)
 "Backward"--z :Always sketch a normal curve first, roughly mark the proportion=area you are given. 
p.84, 3.13 (backward z) Do with table, check using Applet: Normal Density Curve on your CD or at    http://bcs.whfreeman.com/bps5e.
p. 93, 3.53  Quartiles of normal dist.    Use the Applet and also, use table A to find the quartiles. 

YES, all the Below will be assigned Wednesday Day 11 (probably). You can start, sketching and labeling pictures, getting answers with the Applet, standardizing, and leaving space for the final steps of using Table A.
= =  Using table with "x"'s--"raw" values.  = =
 Begin these by drawing and labeling the appropriate normal curve for each question, leaving space for computation.  Normal templates-may help. Then use the Applet: Normal Density Curve on your CD or at   http://bcs.whfreeman.com/bps5e. to find the required values.  Write these on your paper.  Next, standardize the endpoints for each area (proportion) you are asked for. Next we'll calculate the values using Table A.  Your answers from each method should be very close (the Table gives a bit more accuracy than the Applet.)
p. 83, 3.11 Monsoon rains
p. 90, 3.39 Jacob's score
p. 90, 3.43 surprising difference in tails
A. , What proportion of pregnancies last 310 days or more? (Assuming distribution is Normal)  Find Mean and s.d. in p.87, 3.19 ( more next time on this) 
p. 89, 3.34 making tablets (adjust mean)

= = = = POSTPONE Backward Normal - - x problems .= = = =
Begin these by drawing and labeling the appropriate normal curve for each question, leaving space for computation.  Then use the Applet: Normal Density Curve on your CD or at  http://bcs.whfreeman.com/bps5e. to find the required values.  Write these on your paper.   Next we'll calculate the values using Table A.  Your answers from each method should be very close (the Table gives a bit more accuracy than the Applet.)
p. 89-90, 3.36, 3.37, 3.38 Gas Mileage (10th percentile, quartiles, quintiles.  Mean & s.d. are above #3.35)
p. 86, 3.14  quartiles, fruit flies 
====="Approximately" Normal ======
p. 91, 3.47  ACT scores (whole numbers)
p. 92, 3.50 (Use SPSS )  Monsoon rains  If you use Graphs to make the histogram, you can have it put a Normal curve over your histogram.

Read, to discuss

(Before "using table" questions, ) ..
A. Look at table A, pp. 690-1 and compare with the Handout on Densities Cumulative Proportion tables (table A has more numbers; just look at the left 2 columns for now...)  See if you can read from Table A 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.

..
 p. 87, 3.19 pregnancies--68etc rule (This distribution may not apply to planned births, of which we now know there are a lot!)

p. 88, 3.27 Low IQ test scores (68 etc. rule)

 Optional (more practice) 
 


= = = = = = = = 
p. 79 3.8  SAT & ACT (Standardize)

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p. 88 3.26 z's to proportions
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Postpone
"Backward" 
p. 88, 3.29 (backward z)
p. 93, 3.53
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Why do IQ scores trend higher? Read "None of the above" article by Malcolm Gladwell   PDF link   html link    . 
Questions: 1) What is the Flynn effect?
2) What is a likely reason for it?

Exams not finished; Sorry!


"Normal" distributions:("Gaussian", "Bell-shaped") part 1 (pp. 70-74)  Details Day 7   Normal template, optional
Applet: Normal Density Curve   http://bcs.whfreeman.com/bps5e

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
..
Outline:  Details Day 7

Standardizing: (p. 74-5) A "raw value" x is standardized by telling how many standard deviations above the mean it is.
    That's the z-score.  Details Day 7
Values in any Normal distribution, after standardizing, become values in a N(0,1) "standard normal" ("Z") distribution.
(Use double ruler lines on Normal curve, one in "raw" units, one in z.    Normal template, optional)

"What proportion"problems in general:  BPS5e pp. 79-86, first pass
Use  Applet: Normal Density Curve   http://bcs.whfreeman.com/bps5e
   Work toward answering: Proportion with scores between 100 and 145?   below 100?  Above 145?
      Backward: What score is at the 75th percentile?

Use a table. Details Day 7 Written for Z:  N(0,1). Learn to read and use for Z first, then to use for a different mean and s.d.
Standard Normal table use.  Our tables give area to the left of a z value (Cumulative Proportions)
Using standard normal table:  See text p. 81-83. Table A: p.690-1. Table A (Excel)

    Sketch the density, label axis, mark the area you're looking for.
    Figure out how to get it using areas to the left of one or more z-values.
  .Got to here Monday.
Reading table backward: (BPS5e p83-86) Details Day 7
What z value has area ..... to the left/right of it?
               - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
All of these can be checked using the Applet: Normal Density Curve   http://bcs.whfreeman.com/bps5e

Plan for answering general question:  Proportion with scores between 100 and 145?   below 100?  Above 145?
Sketch, with raw and z ruler line. Standardize, finding z-score(s) for the raw edge-value(s).  Find area from table for Standard Normal.  That's your answer.
Preliminary work.  Sketch, mark area, raw and z ruler lines, standardize. Use Applet to find answer.  http://bcs.whfreeman.com/bps5e

  Backward: What score is at the 75th percentile? 
Sketch, with raw and z ruler line.  Mark approximately the area.  Find z-score cutting it off .  UNstandardize to get raw value.
Preliminary work.  Sketch, mark area, raw and z ruler lines. Use Applet to find answer, changing mu and sigma to get both raw and z answer.  http://bcs.whfreeman.com/bps5e

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