Math 151 ,Fall.'07, Mon. Sept. 17, Day 11 Hit Reload...After class.

HW Day 11 (same as day 9)  To do for Wednesday:  Ch. 3 continued. We WILL 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, then reread:  p. 76-80, Cum. proportion and  normal.  "Check" 3.22, 3. 23. "Backward" from prop. to z pp. 81-83.  Read ahead, Ch. 4, 5.

Hand in Wed  --Normal, continued. Normal templates--to count squares!  TableA
----- 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 the Applet: Normal Density Curve on your CD or at   http://www.whfreeman.com/bps4e/, and check with your table answers.  (Uncheck the 2-tail box for most uses. Mean 0, s.d. 1) 
  p.80 3.10 z's to proportions, using Table A.

--------- "Backward"--z ----------
Always sketch a normal curve first, roughly mark the proportion=area you are given. 
p.83, 3.13 (backward z) Do with table, check using Applet: Normal Density Curve on your CD or at http://bcs.whfreeman.com/bps4e. .
p. 89, 3.52  Quartiles of normal dist.    Use the Applet and also, use table A to find the quartiles.  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.

= = = =  Using table with "x"'s--"raw" values. = = = =
 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/bps4e. . to find the required values.  Write these on your paper.  Next, 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. 87, 3.37 Jacob's score, and 3.39 top score. Mean, s.d. are before 3.32 on p. 86.
p. 87, 3.46 surprising difference in tails
 A. , What proportion of pregnancies last 310 days or more? Find Mean and s.d. in p.74, 3.7 (see below **) 
 p. 80-81 3.11 and 3.12 (locomotive adhesion, 2 dist's) 

--(Below here: Separate page--Part of Day 12--we discussed it but I want to give some time for it to sink in.)--
-------- "Backward Normal--x "-----------
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/bps4e. . to find the required values.  Write these on your paper.  Next, 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, 3.14 IQ test
p. 87, 3.41 Abigail, top 20%.  Mean, s.d. are before 3.32 on p. 86.
p. 87, 3.42  quartiles  Mean, s.d. are before 3.32 on p. 86.

p. 179, 7.27 breaking bolts, (a, b +).  For (a), think carefully about which side of 90 you want: Does a bolt that breaks at 95 ksi qualify?  Does a bolt that breaks at 85 ksi qualify?   ALSO:  If they test every bolt and  throw away all bolts that break at 70 ksi or below, what proportion do they throw away?

 Read, to discuss  Optional (more practice) 
 
 p. 86 3.30 z's to proportions
-----------
 

"Backward z" 
p. 86, 3.31 (backward z)
p. 89, 3.53
--------------------



- - - - - - - - -
This is a "backward x" problem:
p. 87, 3.43, quintiles Mean, s.d. are before 3.32 on p. 86.  Quintiles are used by the government to report much economic census data.
- - - - - - - - - - -


Work through the  Normal Probability Practice handout.
**[In 1973] the following item appeared in Dear Abby's column:
     Dear Abby: You wrote in your column that a woman is pregnant for 266 days. Who said so? I carried my baby for ten months  and five days, and there is no doubt about it because I know the exact date my baby was conceived. My husband is in the Navy  and it couldn't have possibly been conceived any other time because I saw him only once for an hour, and I didn't see him again  until the day before the baby was born. I don't drink or run around, and there is no way this baby isn't his, so please print a retraction about that 266-day carrying time because otherwise I am in a lot of trouble.
                                                                               San Diego Reader
Abby's answer was consoling and gracious but not very statistical:

     Dear Reader: The average gestation period is 266 days. Some babies come early. Others come late. Yours was late.

The question here is not whether the baby was late. That fact is already known. At issue is the credibility of the length of the delay. Ten months and five days is approximately 310 days, which means that the pregnancy exceeded the norm by 44 days. [How unusual is that?]

Exams not graded yet. 
= = = = = = = = = = = = = = = = = = =
Applet: Normal Density Curve   http://bcs.whfreeman.com/bps4e
Review: Reading standard normal table forward? Day 8
New:  Reading table "backward"   Day 8
Review: Standardizing   Day 8
Now:  starting with"raw" x's to area:  Day 8, Going from area to x: Day 8
 Handout:  Normal probability practice 

 Recap: "What proportion"problems:  x's to proportions:  Draw picture, label with x's and z's mean, + s.d..  Mark desired area, roughly.
            Standardize  your x's.  Use your z's to look in the table for the area = proportion(s) to the left. 
             Subtract areas (never z's!!) if necessary, to find answer.

"Backward problems"  "What raw (x) value has area ___ to the left/right of it?"   BPS4e pp. 81-83.
        Sketch  the curve, labeled with x values and z values, and the Area, roughly.
        Restate (if needed) as "What z value has area A to the LEFT of it."
        Look in body of table for the value closest to A.
        Go to edge(s) of table to find what z that goes with.
        Convert the z to an x: z is the number of standard deviations above the mean.   x = mean + z ×(s.d.)

We went through all the normal stuff: will answer questions and recap "backward" Wed. Then start Ch. 4.

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