Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 5.5 Normal Approximations to Binomial Distributions Sampling Distributions In 4.2, we learned how to find binomial probabilities. For example, if a surgical procedure has an 85% chance of success and a doctor performs the procedure on 10 patients, Find the probability that exactly 2 are successful. What if the surgical procedure on 150 patients and you want to find the probability of fewer than 100 successful surgeries? I. Normal Approximation to a Binomial Distribution If np >5 and nq ≥5, then the binomial random variable x is approximately normally distributed with mean, u = np Std. Dev., σ npq Example 1 (p260) 1. 2. Do TIY#1 II. Correction for Continuity Binomial Distribution is discrete probability To calculate exact binomial probabilities, use binomial formula for each x value and then add them up Geometrically, this corresponds to adding the areas of bars in the probability histogram Each bar has a width of one unit and x is the midpoint of the interval. To use a continuous normal distribution to approximate a binomial probability, you must Move 0.5 unit to the left and right of the midpoint (x-value) to include all possible x-values in the interval. This is called making a correction for continuity Example 2 (p261) 1. 2. 3. DO TIY#2 III.Guidelines Using Normal Distribution to Approximate Binomial Probabilities 1. 2. 3. 4. 5. 6. 1. Verify that the binomial distribution applies. 2. Determine if you can use the normal distribution to approximate x, the binomial variable. Find the mean u and standard 3. deviation o for the distribution. Apply the appropriate continuity 4. correction. Shade the corresponding area under the normal curve. Find the corresponding z-score(s). 5. Find the probability. 6. Specify n, p and q. Is np > 5? Is nq > 5? u = np o = npq Add or subtract 0.5 from endpoints. z=x–u o Use normalcdf( ?,? ) Example 3 (p262) DO TIY#3 Example 4 (p263) DO TIY#4 Example 5 (p264) DO TIY#5 Homework P265 – 267 #2-8, 20