Содержание
- 2. 7.1 The Standard Deviation as a Ruler Recall that z-scores provide a standard way to compare
- 3. 7.1 The Standard Deviation as a Ruler The 68-95-99.7 Rule In a unimodal, symmetric distribution, about
- 4. 7.1 The Standard Deviation as a Ruler For Example: On August 8, 2011, the Dow dropped
- 5. 7.1 The Standard Deviation as a Ruler Convert the 634.8 point drop to a z-score: A
- 6. 7.2 The Normal Distribution The model for symmetric, bell-shaped, unimodal histograms is called the Normal model.
- 7. 7.2 The Normal Distribution Finding Normal Percentiles When the standardized value falls exactly 0, 1, 2,
- 8. 7.2 The Normal Distribution Example 1: Each Scholastic Aptitude Test (SAT) has a distribution that is
- 9. 7.2 The Normal Distribution Example 1 (continued): Because we’re told that the distribution is unimodal and
- 10. 7.2 The Normal Distribution Example 1 (continued): A score of 600 is 1 SD above the
- 11. 7.2 The Normal Distribution Example 2: Assuming the SAT scores are nearly normal with N(500,100), what
- 12. 7.2 The Normal Distribution Example 2 (continued): First, find the z-scores associated with each value: For
- 13. 7.2 The Normal Distribution Example 2 (continued): Using a table or calculator, we find the area
- 14. 7.2 The Normal Distribution Sometimes we start with areas and are asked to work backward to
- 15. 7.2 The Normal Distribution Example 3 (continued): Since the college takes the top 10%, their cutoff
- 16. 7.2 The Normal Distribution Example 3 (continued): From our picture we can see that the z-value
- 17. 7.2 The Normal Distribution Example 3 (continued): Using technology, you will be able to select the
- 18. 7.2 The Normal Distribution Example 3 (continued): If you need to use a table, such as
- 19. 7.2 The Normal Distribution Example 3 (continued): Convert the z-score back to the original units. A
- 20. 7.2 The Normal Distribution Example: Tire Company A tire manufacturer believes that the tread life of
- 21. 7.2 The Normal Distribution Example: Tire Company A tire manufacturer believes that the tread life of
- 22. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 23. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 24. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 25. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 26. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 27. 7.2 The Normal Distribution Example (continued): Tire Company A tire manufacturer believes that the tread life
- 28. 7.3 Normal Probability Plots The Normal probability plot is a specialized graph that can help decide
- 29. 7.3 Normal Probability Plots The Normal probability plot of a sample of men’s Weights shows a
- 30. 7.4 The Distribution of Sums of Normals Normal models have many special properties. One of these
- 31. For Example: A company that manufactures small stereo systems uses a two-step packaging process. Stage 1
- 32. Normal Model Assumption - We are told both stages are unimodal and symmetric. And we know
- 33. The packing stage, Stage 1, has a mean of 9 minutes and standard deviation of 1.5
- 34. What is the probability that packing an order of two systems takes more than 20 minutes?
- 35. 7.5 The Normal Approximation for the Binomial A discrete Binomial model with n trials and probability
- 36. 7.5 The Normal Approximation for the Binomial Suppose the probability of finding a prize in a
- 37. 7.5 The Normal Approximation for the Binomial For Binomial(50, 0.2), To estimate P(10):
- 38. 7.6 Other Continuous Random Variables Many phenomena in business can be modeled by continuous random variables.
- 39. 7.6 Other Continuous Random Variables The Uniform Distribution For values c and d (c ≤ d)
- 40. 7.6 Other Continuous Random Variables Example: You arrive at a bus stop and want to model
- 41. 7.6 Other Continuous Random Variables Example: You arrive at a bus stop and want to model
- 42. Probability models are still just models. Don’t assume everything’s Normal. Don’t use the Normal approximation with
- 43. What Have We Learned? Recognize normally distributed data by making a histogram and checking whether it
- 44. What Have We Learned? Understand how to use the Normal model to judge whether a value
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