| Hand in:
p. 64 1.61 eyeball sigma p. 54 1.53&54 Normal, men's hts--68-95-99.7 rule. p. 64 1.63 pregnancies--68etc rule -------------------- table use: Always sketch the distribution first, mark the area you are looking for! If you haven't already, Do these with the Statistical Applet "Normal Curve Density Calculator" at http://www.whfreeman.com/scc/ , save to check with table. (Uncheck the 2-tail box for most uses. Mean 0, s.d. 1) Next we learn how to do these with the book's table and the areas methods. (Use table A and the subtracting areas ideas to find these, check with the answers you got from freeman website) p.61 1.57 z's . ------------------- "Backward"Always sketch a normal curve first, roughly mark the proportion=area you are given. p. 62, 1.59 (backward z) Do with table, check with http://www.whfreeman.com/scc/ -------------------- Standardizing: Draw and label the "raw" axis and the "z" axis together, mark your value(s), as well as calculating. p. 56 1.56 SAT/ACT p. 65 1.64 (cf. batting avgs) |
Read, to discuss | Optional
(more practice)
1.55 wechsler ais, 68etc rule --------------------
p. 65 1.65 z's "Backward"
|
Normal distribution. Introduction Day
7
, using 68-95-99.7 rule
Show: "Quincunx" falling bead model for Normal distribution--small
independent influences.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ First standard normal table
use, then standardizing~
~ ~ ~ ~ ~ ~ ~ ~ ~
Standard Normal table use. Our tables give area to the left
of a z value.
Using standard normal table: See text p. 58.
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."
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.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - -
Standardizing: 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.
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: 85 is 1 s.d. below
the mean. Computation: z = (85 –
110)/25
= (–25 raw points)/25
= –1 s.d. from mean.
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
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