A lightbulb has a normally distributed light output with mean 5000 end foot-candles and standard deviation of 50 end foot-candle
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Answer: Normal approximation can be used for discrete sampling distributions, such as Binomial distribution and Poisson distribution if certain conditions are met.
Step-by-step explanation: We will give conditions under which the Binomial and Poisson distribitions, which are discrete, can be approximated by the Normal distribution. This procedure is called normal approximation.
1. Binomial distribution: Let the sampling distribution be the binomial distribution , where
is the number of trials and
is the probability of success. It can be approximated by the Normal distribution with the mean of
and the variance of
, denoted by
if the following condition is met:
2. Poisson distribution: Let the sampling distribution be the Poisson distribution where
is its mean. It can be approximated by the Normal distribution with the mean
and the variance
, denoted by
when
is large enough, say
(however, different sources may give different lower value for
but the greater it is, the better the approximation).