X denotes a binomial random variable with parameters n and

facas9 2021-10-02 Answered
X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
\(\displaystyle{P}{\left({X}={6}\right)}\)

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Expert Answer

Willie
Answered 2021-10-03 Author has 17235 answers

The normal approximation for Binomial probability \(\displaystyle{P}{\left({X}={n}\right)}={P}{\left({n}-{0.5}{<}{X}{<}{n}+{0.5}\right)}\)
Therefore,
\(\displaystyle{P}{\left({X}={6}\right)}={P}{\left({6}-{0.5}{<}{X}{<}{6}+{0.5}\right)}\)
\(\displaystyle{P}{\left({X}={6}\right)}={P}{\left({5.5}{<}{X}{<}{6.5}\right)}\)
Therefore,
\(\displaystyle{P}{\left({X}={6}\right)}={P}{\left({5.5}{<}{X}{<}{6.5}\right)}\)
The area between 5.5&6.5 indicates the appropriate noral curve for binomial probability \(\displaystyle{P}{\left({X}={6}\right)}\)

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