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Statistics 270 - Lecture 15

Learn how to calculate percentiles for normal distributions and their applications. Includes examples and the use of normal approximation to simplify calculations.

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Statistics 270 - Lecture 15

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  1. Statistics 270 - Lecture 15

  2. Percentile for Normal Distributions • The 100pth percentile of the N(m,s2) distribution is m+h(p) s • Where h(p) is the 100pth 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

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