Math 151 , Fall 2002,Wednesday, Sept. 18, Day 9 After class.

Showed: "Quincunx" falling bead model for Normal distribution (it lives in Math Clinic)
          Cardboard model of skewed distribution, which you can balance on pencil to find mean (ask me.)
HW  Day 9  Read  rest of Moore sec. 1.3.
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
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table use: Always sketch the distribution first, mark the area you are looking for!  (Use the table and the subtracting areas ideas to find these, check with the answers you got from   freeman website yesterday.)
p.61 1.57 z's .
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"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/
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Postpone: will be part of day 10 HW. (But you can draw the axes now if you like)
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

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p. 65 1.65 z's
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"Backward" 
p. 65, 1.66 (backward z)
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1.67 
(Activstats--just the parts assigned before)
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Homework questions?

Normal distribution.  Introduction Day 8
   Using standard normal table:  See text p. 58.
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.
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Start here Friday
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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