In a roller-skating rink, the skaters all move at different speeds. Most skate slightly faster or slower than others, but sometimes an adventuresome skater accelerates to an "outlying" speed that is much higher than that of everyone else, creating a hazard. As a result, skating rinks often post a sign that says:

Any skater moving faster than the average speed of all the skaters
will be asked to leave the rink.

It is clear what the sign means, but it is statistically nonsensical. If there are 200 skaters in a rink, all skating at slightly varying speeds, what is the best estimate for how m

Question

In a roller-skating rink, the skaters all move at different speeds. Most skate slightly faster or slower than others, but sometimes an adventuresome skater accelerates to an "outlying" speed that is much higher than that of everyone else, creating a hazard. As a result, skating rinks often post a sign that says:

Any skater moving faster than the average speed of all the skaters 
will be asked to leave the rink.

It is clear what the sign means, but it is statistically nonsensical. If there are 200 skaters in a rink, all skating at slightly varying speeds, what is the best estimate for how m

anonymous · Answer

A. 25 
   B. 0 
   C. 50 
   D. 100 
   E. 75

anonymous · Answer

oops, the last paragraph is incomplete.
It is clear what the sign means, but it is statistically nonsensical. If there are 200 skaters in a rink, all skating at slightly varying speeds, what is the best estimate for how many of them are moving faster than the average speed of all the skaters?

anonymous · Answer

there

anonymous · Answer

methinks it might b 25. but thats just a guess

amistre64 · Answer

im guessing d. 100

amistre64 · Answer

the midrange of 200 is 100 ...

anonymous · Answer

amistre how did u get that?

anonymous · Answer

amistre ur a freaking genius :P

amistre64 · Answer

im assuming the speeds are normally distributed and that .5 is the probablitity of less then the mean and .5 the probability of above the mean; 200*.5 = 100 ... just a guess tho

amistre64 · Answer

suppose we test this on 5 skaters; 2,3,6,9,13 are the speeds; if we select all the samples of 2, with replacement we get:

\begin{array}c
2,2&3,2 &6,2 &9,2 &13,2 &\
2,3&3,3 &6,3 &9,3 &13,3 &\
2,6&3,6 &6,6 &9,6 &13,6 &\
2,9&3,9 &6,9 &9,9 &13,9 &\
2,13&3,13 &6,13 &9,13 &13,13 &\
\end{array}

the means of these are:

2.......1 ;  2
2.5 ...2 ;  5
3 ..... 1 ;  3
4 ......2 ;  8
4.5....2 ;  9
5.5....2 ;11
6 ..... 3 ;18
7.5....4 ;30
8 ......2 ;16
9 ..... 1 ;  9
9.5....2 ;19
11 ....2 ;22
13.....1 ;13
           -----
            165/25 = 6.6 for a mean

2+3+6+9+13
------------- = 6.6 for a mean :)
         5

6.6 is our mean; and we have 2,3,6 below; and 9,13 above ...so its about half and half was the sample size gets larger