If n=15 and P=0.1, would normal distribution provide accurate probabilities?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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If n=15 and P=0.1, would normal distribution provide accurate probabilities?
Transcribed Image Text:If n=15 and P=0.1, would normal distribution provide accurate probabilities?
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Step 1
  • Normal to binomial approximation : 

For a random variable  with a Binomial distribution with parameters  and , the population mean and population variance are computed as follows:

When the sample size  is large enough, and/or when  is close to 12, then  is approximately normally distributed. But in order to approximate a Binomial distribution (a discrete distribution) with a normal distribution (a continuous distribution), a so called continuity correction needs to be conducted. Specifically, a Binomial event of the form

\Pr(a \le X \le b)

will be approximated by a normal event like : 

\Pr(a - \frac{1}{2} \le X_{Normal} \le b + \frac{1}{2})

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