MATH 251, Probability and Statistics I, Fall 2001, Day 6

Day 6, Wednesday Sept. 12  [stuff in brackets will be assigned Day 7--these all use the table "backwards."  Try them, but put them on separate paper.]
Reading: Normal distribution, pp.70-79.  Optional: SPSS manual, p.53-56
Read ahead:  Normal quantile plots, 79-85; then Ch. 2
Hand in: 
p. 86, 1.73 (sketch, EPA) 1.75 middle 95%
1.77 pregnancies
1.78 mean= 108.92, s=13.17, table p. 33. cf. shape.
1.80 batting; cf z's
1.82,[ 84] (standard normal table)
Non-standard normal, table problems: 
    X is normal with mean 3 and s.d. 2. Find: 
    The relative frequency of X<1.5.  1.5 < X < 4.5. 
    [The x for which 30% of the observations are 
              smaller than it. The 30th percentile. ]
1.89 hypokalemia?
1.93, [94] (Wechsler WISC)
p.96 1.113d  3rd &6th grade again
[p. 90 1.95 quartiles etc. ]
B.  What percent of pregnancies last 310 days? 
    (cf. 1.77, see quote below) 
Read, discuss 
 
 

1.79 
1.81, 83 (more table practice)

Optional 
1.74 (sketch)1.76 
 
 
 
 
 

[<--Find the x for which 80% of the observations are smaller than it.  The 80th percentile.] 
>Find answers to normal table problems with SPSS (manual pp. 53-4) 
 

 

[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?]

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