Drama
Money in a Texas hat
After taking my course, Nick, an
entrepreneurial mind, decided to go
into business. He went south to
Houston Texas, and planned a
betting business without any
substantial investment. Just an
antique Texas Instruments
calculator. For two months he stood
at a corner in downtown Houston
asking every man that appeared
around the corner:
Excuse me, sir, would you mind if I
measure how tall you are? I am
running my thesis and need data.
He carefully recorded the data. At
the end of the two months he had
measured the heights of 4000 men.
Now he punched his data into the
calculator and computed the mean
and the standard deviation.
The mean was 170 cm, that is 1
meter and 70 centimeters. The
standard deviation was 10.
The next morning, he puts on his
brightest face, and stands at the same
corner in downtown Houston. Time to
make money.
Excuse me sir, I bet $1000.00 that the
first man that will appear around the
corner will be between 1 meter 50
centimeters, and 1 meter 90
centimeters tall.
Not all passersby pay attention to him
but a few do.
Oh Yeah? How do you know, buddy?
You think you are smart, ah? Here is
$1000. Show me yours.
Tom puts down his $1000. Here he
comes, first man appears around the
corner. He agrees to be measured. His
height is 170. Nick wins. Nick will
make several thousand dollars on his
first day. He loses a few times but
95% of the time he wins.
Let’s see his reasoning.
He followed my example of
Basita’s story. He placed the mean
of the heights,170 cm, (the one
that he computed from his data)
on the middle of the normal curve.
Now he reasoned that since the
standard deviation of his data was
10, at standard deviation -1 score
160 exists, at standard deviation
-2 score 150 exists, and at
standard deviation -3 score 140
exists.
Similarly, on the right side of the
curve, score 180 is at standard
deviation +1, score 190 is at
standard deviation +2, and score
200 is at standard deviation +3.
One more example:
Mean 20
Standard deviation 3
What standard deviation score 26
lies at?
Answer: Score 26 lies at standard
deviation +2
At standard deviation +1 we have
score 23, i.e., 20+3
At standard deviation +2 we have
score 26, i.e., 20+3+3
At standard deviation +3 we have
score 29, i.e., 20+3+3+3
At standard deviation -1 we have
score 17, i.e., 20-3
At standard deviation -2 we have
score 14, i.e., 20-3-3
At standard deviation -3 we have
score 11, i.e., 20-3-3-3