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Unformatted text preview: to calculate P( x > a), P( x < a) , we can
standardize the interval of interest in terms of
zvalues:
a−µ
z=
σ/ n Example: Body Temperature Suppose the temperatures of healthy humans is
approximately normal with a mean of 98.6 degrees
and a standard deviation of 0.8 degrees
If 130 healthy people are selected at random, what
is the probability that the average temperature for
those people is lower than 98.25 degrees?
Answer: Sampling Distribution of Sample
Proportion
The Central Limit Theorem implies that the binomial (n, p)
random variable X is approximately normal when n is large, with
mean np and standard deviation np(1 − p) ˆ
The sample proportion p, is simply a rescaling of the binomial
ˆ
random variable X: p = X/n
From the Central Limit Theorem, the sampling distribution of
is also approximately normal, with a rescaled mean p and
standard deviation (standard error) p(1 − p) / n Example: Intel In 1996, Intel shipped 76% of the microprocessor market...
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 Fall '10
 samaniego
 Statistics, Central Limit Theorem, Standard Error

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