| Hand in:
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!) p. 88, 3.51 check 68-95-99.7 rule , using applet: Normal Density Curve on your CD or at http://www.whfreeman.com/bps/. - - - - - Standardize: Draw and label the normal density curve, the "raw" axis and the "z" axis together, mark your value(s), as well as calculating. p. 76, 3.9 mens & women's heights p. 86, 3.33 ACT/SAT Jacob and Emily (Info is above #3.32) Exam is to here. -------------------- Postpone the rest: Table use: 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/bps/, 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"Always sketch a normal curve first, roughly mark the proportion=area you are given. p.86, 3.13 (backward z) Do with table, check using Applet: Normal Density Curve on your CD or at http://www.whfreeman.com/bps/. 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. |
Read, to discuss | Optional
(more practice)
---------------- p. 86 3.30 z's to proportions "Backward"
|
Jennifer writes: ...changing my hours this week because of the test on Friday. I will be in the math clinic Tuesday from 2-5pm and Wednesday 6-7:30pm. If these hours are not convenient let me know and we can set up an individual appointment. joneill@wells.eduSolutions manual (finally!) will be in the Math Clinic this afternoon, as soon as I can get it photocopied. (Manual truncates Stemplots instead of rounding!)
Normal distribution. Introduction Day
7
, using 68-95-99.7 rule, standardizing. Applet:
Normal Density Curve http://www.whfreeman.com/bps/
Start here next time
Show: "Quincunx" falling bead model for Normal distribution--small
independent influences.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Standard
normal table
use~
~ ~ ~ ~ ~ ~ ~ ~ ~
Standard Normal table use. Our tables give area to the left
of a z value (Cumulative Proportions)
Using standard normal table: See text p. 76-80. Table
A, p.684-5.
z |
.00 .01 .02
.....
...|
1.4 | .9192 .9207
.9222 ....
P(z < 1.40) = .9192, P(z < 1.41)
= .9207 P(z < 1.42) = .9222.
?z has more than 2 dec. places? Round to 2.
Sketch the density, mark the area
you're looking for.
Figure out how to get it using areas to
the left of one or more z-values.
Think cutting up paper
bell-curves.
(Remember whole area is 1.)
Example: Proportion of observations between 0.5 and
1.4
P(0.5 < z <1.4) =
Proportion of observations below 1.4 minus
Proportion
of observations below 0.5
P (z < 1.4) - P(z < 0.5) = .9192 - .6915 =
.2277
.
Reading table backward:
What z value has area ..... to the left/right
of it?
Sketch 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.
Example: "What z value has 10%
of the observations above it?" This is the same z as the one for:
"What
z value has 90% of the observations below (to the left of) it?"
"What z value is at the 90th percentile?"
Find
in the table .8997 and .9015 -- .9000, our number, is
between them.
.8997 is a little closer to.9000, so use it.
For .8997, the z value is 1.28.
1.28 has 10% of the observations above it.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - -
All of these can be checked using the Applet:
Normal Density Curve http://www.whfreeman.com/bps/
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