solution=
2000 is the best choice. (option c)
The most likely standard deviation is 2000 ,since the band most
likely played
to a very large audience once in addition to the normal smaller
crowds.
This would put about 2 in 3 concerts (2/3 is quite close to 68%)
with
attendance between 19359 and 23359 and most (95%) between 17359 and
25359. A standard
deviation of 20000 would imply about 68% of shows having between
359 and 41,359 as
attendance – and the problem states that concerts always drew a
large crowd (values about 360
are ruled out). A standard deviation of 20 makes the attendance
within 60 of 21,359 for almost
all concerts, which is hard to believe. A standard deviation of 200
is not the worst answer (partial
credit), but if that’s the value then attendance never falls
outside of 20,759 to 21,959, which is
still a fairly narrow range – especially given that the band would
be playing in venues (arenas,
probably) of a variety of capacities.
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