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 \(\displaystyle{P}{\left({X}\geq{8}\right)}\)