The Normal Approximation to the Binomial Distribution:
© Rita Marie O’Brien Chapter 6.4 Page 2 The Normal Approximation to the Binomial Distribution We have learned how to find binomial probabilities. For instance, if a surgical procedure has an 85% chance of success and the doctor performs this procedure on 10 patients it is easy to find the probability of exactly 2 successful surgeries.
The Normal Approximation to the Binomial Distribution:
© Rita Marie O’Brien Chapter 6.4 Page 3 The Normal Approximation to the Binomial Distribution But, what if the doctor performs the procedure on 150 patients and you must find the probability of fewer than 100 successful surgeries. To find this you would use the binomial formula 100 times and find the sum of the resulting probabilities. This approach is not practical, of course, a better way is to use a normal distribution to approximate the binomial distribution.
The Normal Approximation to the Binomial Distribution:
© Rita Marie O’Brien Chapter 6.4 Page 4 The Normal Approximation to the Binomial Distribution If (p = success and q = failure), then the binomial random variable x is approximately normally distributed, with and the standard deviation .
The Normal Approximation to the Binomial Distribution:
© Rita Marie O’Brien Chapter 6.4 Page 5 The Normal Approximation to the Binomial Distribution When you use a continuous normal distribution to approximate a binomial probability, you need to move .5 units to the left and right of the midpoint to include all possible x – values in the interval. When you do this, you are making a correction for continuity.
The Normal Approximation to the Binomial Distribution:
© Rita Marie O’Brien Chapter 6.4 Page 6 The Normal Approximation to the Binomial Distribution