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Solutions to PS #2
5.20)
Our data has a Gaussian distribution, with a mean of 69” and a standard deviation
of 2”.
Given a random sample of 1000 people, how many are a) 6771”, b) > 71”,
c) > 75”, d) 6567”?
a) This is just the integral covering one standard deviation on both sides.
From
Appendix A, we get that this corresponds to 68.27%, which is about 683 people.
b) First we figure out how many people aren’t
within one standard deviation, which
is equal to (1 – 68.27%), or 31.73%.
Half of these are above 71”, and half are
below 67”.
So percentage above is 0.5*31.73%, which corresponds to 15.865%,
or about 159 people.
c) Like b, except now it’s three standard deviations.
Percentage > 75” or < 63” is
equal to (1 – 99.73%), or 0.27%.
Half this is 0.135%, which is about 1 person in
our sample of 1000.
d) Now we want to know how many people are between one and two standard
deviations short.
Break this up into pieces:
95.45% are within 2 standard
deviations on either side, half of this is people between 65” and 69” (47.725%).
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 Spring '04
 boering

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