X denotes a binomial random variable with parameters n and

Tahmid Knox 2021-10-02 Answered
X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
\(\displaystyle{P}{\left({X}≥{8}\right)}\)

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Expert Answer

Lacey-May Snyder
Answered 2021-10-03 Author has 14985 answers

Step 1
Continuity corection:
The binomial probability is converted to a normal distribution probability by using the continuity correction.
f the binomial probability represents \(\displaystyle{X}\geq{a}\) then subtract 0.5 from a and 0.5 to n where n represents the number of trials.
That is,
\(\displaystyle{P}{\left({X}\geq{8}\right)}={P}{\left({8}-{0.5}{<}{x}{<}{n}+{0.5}\right)}={P}{\left({7.5}{<}{x}{<}{n}+{0.5}\right)}\)
Thus, the area between 7.5 and \(\displaystyle{n}+{0.5}\) under the appropriate normal curve would estimate the binomial probability \(\displaystyle{P}{\left({X}\geq{8}\right)}\)

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