4. Suppose the messiness of apartments is measured on
a scale from 0 to 100, with 0 the cleanest and 100 the
messiest. Suppose also that the distribution of apart-
ments by messiness is as shown in the diagram. That
is, suppose 10 percent of the apartments lie between
0 and 20, 20 percent between 20 and 40, and so on.
10%
40%
20%
20%
10%
Cleanest
Messiest
0 20 40 60 80 100
Suppose, finally, that all parents tried to teach their
children never to let anyone in to see their apartments
if they were over 80 on the messiness scale.
(a) If such a rule of thumb were widely observed,
what would be your best estimate of the messi-
ness index of some-one who said, \"You can't
come in now, my place is a pit\"?
(b) In a world in which everyone makes use of all
available information, would you expect this rule
of thumb to be stable?
(c) What do you conclude from the fact that peo-
ple really do sometimes refuse admission on the
grounds that their apartments are too messy?
