1. Statistics 270 - Lecture 15

2. Percentile for Normal Distributions The 100p th percentile of the N( ,  2 ) distribution is  +  (p)  Where  (p) is the 100p th percentile of the standard normal Proof:

3. Why is this useful?

4. Example Find the 97.50 percentile of the N(10,5) distribution

5. Example Verbal SAT scores follow approximately a N(430, 100) distribution What is the interval that encompasses the middle 50% of scores

6. Normal Approximation to the Binomial If X has a Binomial(n, p) distribution and n is large, then the calculations for this distribution become cumbersome (e.g., P(X<100) ) If X has a binomial distribution with parameters n and p, with np 5 and n(1-p) 5, then X has approximately a distribution

7. Normal Approximation to the Binomial Recall, Can use Poisson approximation when Can use Normal approximation when

8. Continuity Correction

9. Example Suppose that 25% of all licensed drivers in a particular province do not have insurance Let X be the number of uninsured drivers in a random sample of size n = 50

10. Example Suppose that 25% of all licensed drivers in a particular province do not have insurance Let X be the number of uninsured drivers in a random sample of size n = 50