p. 63, 1.105 & 106 test scores, proportions
C. A small difference in means may give a surprisingly
large proportional difference in tails:
p. 69, 1.109&10: Sketch Normal; shift and stretch
1.121 Use Normal Density Curve Applet to check on the Rule
1.23 (horse preg's , rule)
Postpone the rest:
1.127 (forward), 1.129 (backward) (standard normal table, more practice)
1.130 & 131 (Wechsler WAIS, more practice)
Use Normal Density Curve Applet http://www.whfreeman.com/ips7e/ (or theapplet for ips6e, etc.) to check on all your Normal calculations! (The Applet goes by .02's, and the text by .01's so the answers may differ slightly)
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.Abby's answer was consoling and gracious but not very statistical:San Diego Reader
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?]
Standardizing: A way of comparing an individual
Comparing individuals from different packs, each relative to its own.
Removes "units of measurement" from the discussion.
Enables use of the standard normal table.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ First standard normal table use, then with "real" values~ ~ ~ ~ ~ ~ ~ ~ ~ ~
OPTIONAL aids: Normal curve template (you can count squares), Normal practice handout
Standard Normal N(0, 1). Our tables give area to the left of a z value. Table A, front flyleaf
Using standard normal table: p. 77
z | .00 .01 .02 .....
1.4 | .9192 .9207 .9222 ....
P(Z < 1.40) = .9192, P(Z < 1.41) = .9207 P(Z < 1.42) = .9222.
Find desired area above or between by rewriting as a
subtraction involving area(s) to the left of the endpoint(s).
. Reading table "backward":
What z value has area ..... to the left/right of it?
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 is 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 is the 90th percentile.
1.28 has 10% of the observations above it.