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DUE Date: 9/23
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Homework #3
When a series of values takes on some distribution, it is common to describe it in terms of
a distribution and parameters that fit the data.
IQ tests, for example, are rescaled so that
results are normally distributed with a mean of 100 and a standard deviation of 15.
Taken a step further, this implies that about 99.5% of people who take an IQ test will get
a score between 55 and 145, about 95% will score between 70 and 130, and so on.
The
variance for such a test would be 225, so we might write that IQ ~ Normal(100, 225).
1) In a normal distribution, what proportion of the scores fall within the interval between
μ
and one standard deviation above
μ
?
(Equivalently, in the IQ example above, what
fraction of the population would you expect to score between 100 and 115?)
a. .8413
b. .6826
c. .4143
d. .1359
e. .3414
2) In a normal distribution, .9544 of the scores will be located in the interval between __.
a.
μ
plus 2σ
b.
μ
plus 1σ and
μ
minus 2σ
c.
μ
plus 2σ and
μ
minus 3σ
d.
μ
plus 2σ and
μ
minus 2σ
e.
μ
plus 1σ
3) If a distribution is normal with µ = 50 and σ = 10, then what proportion of the scores
will fall between 40 and 60 (µ
±
σ)?
a. .1359
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 '07
 Nezami,Borovay

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