In Exercises, X denotes a binomial random variable with parameters n and p. For each...

Step 1
Continuity correction:
The binomial probability is converted to a normal distribution probability by using the continuity correction. Step 2
If the binomial probability represents ${\displaystyle a<X<b}$ then add 0.5 to a and subtract 0.5 with b.
That is,
${\displaystyle P\left(7<X<10\right)=P(7+0.5<x<10-0.5)=P\left(7.5<X<9.5\right)}$
Step 3
Thus, the area between 7.5 and 9.5 under the appropriate normal curve would estimate the binomial probability ${\displaystyle P\left(7<X<10\right).}$