1 / 16

Unit 4 – Probability and Statistics

Unit 4 – Probability and Statistics. Section 12.7 Day 10. Warm-Up. Using the given data set: 77, 76, 83, 88, 90, 85, 81, 77, 95, 89 Find the mean, median, mode Find the range and interquartile range Create a box-and-whisker plot of the data

liuz
Download Presentation

Unit 4 – Probability and Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit 4 – Probability and Statistics Section 12.7 Day 10

  2. Warm-Up Using the given data set: 77, 76, 83, 88, 90, 85, 81, 77, 95, 89 • Find the mean, median, mode • Find the range and interquartile range • Create a box-and-whisker plot of the data • Find the standard deviation (Show all your work.)

  3. Warm-Up Answers Data set in order: 76, 77, 77, 81, 83, 85, 88, 89, 90, 95 • Mean = 84.1; Median = 84 ; Mode = 77 • Range = 19; Interquartile range = 12 • Create a box-and-whisker plot of the data • Standard deviation σ = 6.1

  4. Section 12.7 Normal Distributions Goal: calculate probabilities using normal distributions Normal Curve – symmetrical bell-shaped curve Important symbols • σ (Sigma) represents standard deviation • x (x-bar) represents mean

  5. Section 12.7 Normal Distributions Important Aspects of a Normal Curve • Total Area under the curve is 1 • 68% of the area lies within 1 standard deviation of the mean • 95% of the area lies within 2 standard deviations of the mean • 99.7% of the area lies within 3 standard deviations of the mean

  6. Section 12.7 Normal Distributions 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% -3σ -2σ -σ x +σ +2σ +3σ

  7. Example 1 The price of sandals is normally distributed with a mean of $36 and a standard deviation of $9. • What percent were priced between $18 and $72? • What is the probability that a randomly chosen pair is priced between $9 and $18?

  8. Example 1 (cont.) 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% $9 $18 $27 $36 $45 $54 $63 A) What percent were priced between $18 and $72? 97.5%

  9. Example 1 (cont.) 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% $9 $18 $27 $36 $45 $54 $63 B) What is the probability that a randomly chosen pair is priced between $9 and $18? 2.35%

  10. Example 2 The weight of strawberries packed in a medium-sized container was normally distributed with a mean of 16.18 ounces and a standard deviation of 0.34 ounce. • If you randomly choose 2 containers of strawberries, what is the probability that both weigh less than 15.5 ounces? • If you randomly choose 2 containers of strawberries, What is the probability that both of the containers weighs at least 15.84 ounces? • If you randomly choose 2 containers of strawberries, that one container weighs between 15.5 and 15.84 ounces, and the 2nd container weighs at least 16.86 ounces?

  11. Example 2 (cont.) 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% (oz.) 15.16 15.5 15.84 16.18 16.52 16.86 17.2 A) Both containers weigh less than 15.5 oz? 0.025 0.025 = 0.000625 or 0.0625%

  12. Example 2 (cont.) 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% (oz.) 15.16 15.5 15.84 16.18 16.52 16.86 17.2 B) Both containers weigh at least 15.84 oz? 0.84 0.84 = 0.7056 or 70.56%

  13. Example 2 (cont.) 34% 34% 13.5% 13.5% 0.15% 0.15% 2.35% 2.35% (oz.) 15.16 15.5 15.84 16.18 16.52 16.86 17.2 C) Between 15.5 and 15.84 oz and at least 16.86? 0.135 (0.0235 + .0015) = 0.003375 or 0.3375%

  14. PRACTICE P. 749-750 #19 - 28

  15. PRACTICE ANSWERS 19) 50% 20) 15.85% 21) 2.5% 22) 27% 23) 0.68 24) 0.4985 25) 0.9735 26) 0.84 27) 0.84 28) 0.975

  16. HOMEWORK P. 750-751 #29 – 31, 38 - 49

More Related