Section 5.5: Normal Approximation to the Binomial Distribution
The premise in our Larson textbook for using the normal approximation is that finding the binomial probability of an “less than x” or “greater than x” problem would be onerous – having to manually calculate each of the discrete values and then sum them up. They give an example of a doctor who performs a surgery that has an 85% success rate, but you want to know the probability that fewer than 100 of 150 attempted surgeries will be successful. And yes, finding each of the 101 discrete values (0 to 100) would be time-consuming if done manually using the equations in the book.
But, the reality today is that our software can easily do that – Excel, StatCrunch, and I think even the TI. Those software “technology” tools can find the cumulative probability from the left tail to the value of x we need. So, in the “real” world today, you would rarely, if ever, need to use the normal approximation to the binomial and its concomitant continuity correction.
Remember, the normal is an approximation and not as precise as using the true binomial distribution.
That said, for this academic course, you do need to know how to use the normal approximation to the binomial at least for the homework. I have a blog post on the details of doing this for a problem from Section 5.5 here https://www.drdawnwright.com/?p=16678
I also have an online Excel calculator that makes this easy to do here https://www.drdawnwright.com/?p=17877
