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Lecture 10.4 b bt

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  • 1. Today’s Agenda  Attendance / Announcements  Sections 10.4b  Have a good Holiday!
  • 2. Exam Schedule  Exam 5 (Ch 10) Thur 12/5  Final Exam (All) Thur 12/12 1 hour, 50 mins
  • 3. The Normal Curve
  • 4. The Normal Curve
  • 5. The Normal Curve
  • 6. The Normal Curve
  • 7. The Normal Curve Z-scores:
  • 8. The Normal Curve The following are synonymous when it comes to the normal curve: • Find the area under the curve … • Find the percentage of the population … • Find the probability that …
  • 9. The Normal Curve
  • 10. Using a Z-Table to find probabilities Note: Our Z-table only gives area to the left (or probabilities less than z)
  • 11. The Normal Curve Find Probability that z < 0.97 P(z Find area under the curve to the left of z = 0.97 0.97) Z-scores: -3 -2 -1 0 1 0.97 2 3
  • 12. Using a Z-Table to find probabilities Find Probability that z < 0.97 Since z > 0, use positive side
  • 13. The Normal Curve Find Probability that z < -2.91 Z-scores: -3 -2.91 -2 Find area under the curve to the left of z = -2.91 -1 0 1 2 3
  • 14. Using a Z-Table to find probabilities Find Probability that z < -2.91 Since z < 0, use negative side
  • 15. Using a Z-Table to find probabilities • Not all Z-Tables are alike!
  • 16. Using a Z-Table to find probabilities • But we can still use our z-table to find areas to the right (probability greater than), as well as areas between two values (probability between two values).
  • 17. The Normal Curve Find Probability that z > 0.75 Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 -1 0 1 0.75 2 3
  • 18. Finding Area to the Right • Two Methods –Using the Complement of 1 –Using Symmetry
  • 19. Complement Method Find Probability that z > 0.75 Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 -1 0 1 0.75 2 3
  • 20. Complement Method Use fact that area under entire curve is 1. And that we can find area to the left Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 -1 0 1 0.75 2 3
  • 21. Complement Method Use fact that area under entire curve is 1. And that we can find area to the left Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 -1 0 1 0.75 2 3
  • 22. The Normal Curve Find Probability that z > 0.75 Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 -1 0 1 0.75 2 3
  • 23. Symmetry Method
  • 24. Symmetry Method Use symmetry of the normal curve to find area Z-scores: -3 -2 Find area under the curve to the right of z = 0.75 1 -1 0 - 0.75 0.75 2 3
  • 25. Finding Area between two values • Just use difference of the two areas
  • 26. Difference of Area Find Probability that -1.25 < z < 0.75 Z-scores: -3 Find area under the curve between -1.25 and 0.75 -2 -1 -1.25 0 1 0.75 2 3
  • 27. Finding Probabilities of Normal Distributions 1. For data that is normally distributed, find the percentage of data items that are: a) below z = 0.6 b) above z = –1.8 c) between z = –2 and –0.5
  • 28. Finding Probabilities of Normal Distributions 2. Given a data set that is normally distributed, find the following probabilities: a) P(0.32 ≤ z ≤ 3.18) b) P(z ≥ 0.98)
  • 29. Solving Applications of Normal Distributions Before solving real world applications of data that is normally distributed, we need to first calculate any appropriate z-scores based on the data. This is called normalizing the data.
  • 30. Solving Applications of Normal Distributions Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. After converting each reading to its z-score, find the percentage of people with the following blood pressure readings: a) below 142 b) above 130 c)between 142 and 154
  • 31. Solving Applications of Normal Distributions A machine produces bolts with an average diameter of 7 mm and a standard deviation of 0.25 mm. What is the probability that a bolt will have a diameter greater than 7.1 mm? Assume the distribution is normal.
  • 32. Solving Applications of Normal Distributions The placement test for a college has scores that are normally distributed with = 500 and = 100. If the college accepts only the top 10% of examinees, what is the cutoff score on the test for admission? (hint: you’ll need to use the table first, and work backwards)
  • 33. Classwork / Homework • 10.4 Worksheet • Page 638 • 1 – 4, 9 – 19 odd, 25 – 35 odd