# 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. P(X >= 8)

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.
$P\left(X\ge 8\right)$
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Step 1
Continuity correction:
The binomial probability is converted to a normal distribution probability by using the continuity correction.
If the binomial probability represents “$$\displaystyle{X}\ge{a}$$” then subtract 0.5 from a and 0.5 to n where n represents the number of trials.
Step 2
That is,
$$\displaystyle{P}{\left({X}\ge{8}\right)}={P}{\left({8}-{0.5}{<}{X}{<}{N}+{0.5}\right)}$$
$$\displaystyle={P}{\left({7.5}{<}{X}{<}{N}+{0.5}\right)}$$
Thus, the area between 7.5 and $$n+0.5$$ under the appropriate normal curve would estimate the binomial probability $$\displaystyle{P}{\left({X}\ge{8}\right)}$$.