Homework 2 Solutions

Ch. 4:

6. (a) average 40 - hist(iii)
       average 50 - hist(ii)
       average 60 - hist(i)

   (b) median less than average hist(iii)
       median about equal to average hist(ii)
       median greater than average hist(i)

   (c) SD is around 15.

   (d) False: the SDs for histograms (i) and (iii) are about equal.
They have similar spreads, they're just skewed to opposite sides (like
mirror images of each other).



Ch. 5: 

4.  (a) 20%      (b) 12%
 
7.  Scores on the Math SAT had an average of 500 and a SD of 100.

    (a) A student who scored 350 was at the 7th percentile of the
score distribution.  350 is (500-350)/100=1.5 SDs below the average of
500, and the area to the left of -1.5 under the normal curve is 7%.

    (b) To be at the 75th percentile, a student would need to have
scored about 570 points.



Ch. 8: 

1.  Plot (d) represents this study best.  Plot (a) is not accurate
because it shows average IQs for both husbands and wives much lower
than 100 (maybe 50 or so).  Plot (b) shows IQs for both genders with
SDs less than 15.  Plot (c) shows a correlation coefficient higher
than r=0.6 (can see this by the tight clustering of points around the
line); also, the SDs are too big.  Plot (d) resembles reasonable-seeming
representations of averages, SDs, and correlation.

3.  The correlation would be 1, since y=0.92x (y=wife's height,
x=husband's height).  This means all the observations would fall on
this line, and if we knew the height of either member of the couple,
we could predict the height of the other exactly.