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)

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 \(\displaystyle{P}{\left({X}\ge{8}\right)}\).