Suppose the lifetime of incandescent light bulbs has a mean of 1691.805 hours and a standard deviation of 79.1675 days. According to the Central Limit Theorem, what happens to the histogram of averages as n increases?
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Suppose the lifetime of incandescent light bulbs has a mean of 1691.805 hours and a standard deviation of 79.1675 days. According to the Central Limit Theorem, what happens to the histogram of averages as n increases?
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The correct answer is:
2) The histogram will begin to look more like the normal
curve.
According to the central limit theorem, if X1,X2,...XN are a
sequence of iid random variables with finite mean
and finite non-zero variance
, then the distribution of
as n tends to infinity.
In other words, the histogram of averages as n increases would start looking more and more like the normal curve.
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