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Section 6.2 PART 1 STATISTICS

Section 6.2 PART 1 STATISTICS. Notes – Section 6.2 PART 1 Standard Units and Areas Under the Standard Normal Distribution Homework due Tuesday: A#6.21 pages 256 – 258 #8 - 28 even. Monday February 24. Section 6.2 – Standard Units and Areas Under the Standard Normal Distributions.

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Section 6.2 PART 1 STATISTICS

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  1. Section 6.2PART 1STATISTICS • Notes – Section 6.2 PART 1 • Standard Units and Areas Under the Standard Normal Distribution • Homework due Tuesday: • A#6.21 pages 256 – 258 #8 - 28 even Monday February 24

  2. Section 6.2 – Standard Units and Areas Under the Standard Normal Distributions After this section, you will be able to: • Convert raw data to z scores; • Convert z scores to raw data; • Graph the standard normal distribution and find areas under the standard normal curve.

  3. Differences in Normal Distributions 1. The mean may be located anywhere on the ________________________, and 2. The ______________________________ may be more or less spread according to the size of the __________________________________________________. …causes difficulties when computing the ______________ under the curve in a specified interval of x values

  4. z Scores The z valueor z score give the number of _____________________________ between the _____________________ measurement x and the ____________________of the x distribution.

  5. Example: Standard Score Little Bambinos pizza franchise specifies that the average amount of cheese on a large pizza should be 8 ounces and the standard deviation only 0.5 ounce. An inspector picks out a large pizza at random in one of the pizza parlors and finds that it is made with 6.9 ounces of cheese. Assume that the amount of cheese on a pizza follows a normal distribution. If the amount of cheese is below the mean by more than three standard deviations, the parlor will be in danger of losing its franchise. How many standard deviations from the mean is 6.9? Is the pizza parlor in danger of losing its franchise?

  6. Raw Scores Given an x distribution with __________ and ____________________________, the raw scorex corresponding to a z score is:

  7. PRACTICE: Standard Score and Raw Score Rod figures that it takes an average (mean) of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to an early-morning class. A. One day it took Rod 21 minutes to get to class. How many standard deviations from the average is that? Is the z value positive or negative? Explain why is should be either positive or negative. B. What commuting time corresponds to a standard score of ? Could Rod count on making it to class in this amount of time or less?

  8. The Standard Normal Distribution

  9. Table 5 – Appendix II • Pages A22 and A23 in your text • Left-tail style table

  10. PRACTICE: Standard Normal Distribution Table Use Table 5 of Appendix II to find the described areas under the standard normal curve. Find the area under the standard normal curve to the left of Insert fig 6.16 Insert table 6-3

  11. PRACTICE: Standard Normal Distribution Table b. Find the area to the left of . Insert fig 6.17 Insert table 6-4

  12. PRACTICE: Using the Standard Normal Distribution Table Looking at Table 5 in Appendix II: As z values increase, do the areas to the left of z increase? If a z value is negative, is the area to the left of z less than 0.5000? If a z value is positive, is the area to the left of z greater than 0.5000?

  13. Finding areas other than to the left For areas to the left of a specified z value, __________________________________________ For areas to the right of a specified z value, _________________________________________ For areas between two z values,and (where ) _______________________________ • Hints: • Round or format z values to 2 decimal places before using the table • Treat any area to the left of a z value smaller than -3.49 as 0.000 • Treat any area to the right of a z value greater than 3.49 as 1.000

  14. Insert fig 6-18

  15. PRACTICE: Using the Standard Normal Distribution Table Use Table 5 of Appendix II to find the described areas under the standard normal curve. Find the area between and

  16. PRACTICE: Using the Standard Normal Distribution Table Use Table 5 of Appendix II to find the described areas under the standard normal curve. b. Find the area to the right of

  17. Warm-up – Page 257 #9 • Check in and go over A#6.21 • Notes – Section 6.2 – PART 2 • Probabilities associated with the Standard Normal Distribution • Homework due Wednesday: • A#6.22 pages 256 – 258 • #1-7 all; 30-48 even Section 6.2PART 2STATISTICS Tuesday February 25

  18. WARM-UP: Page 257 # 9

  19. PRACTICE: Using the Standard Normal Distribution Table Let z be a random variable with a standard normal distribution. a. refers to the probability that z values lie to the right of 1.15. Shade the corresponding area under the standard normal curve and find

  20. PRACTICE: Using the Standard Normal Distribution Table Let z be a random variable with a standard normal distribution. b. Find . First, sketch the area under the standard normal curve corresponding to the area.

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