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Warm-Up

Warm-Up. Grab a sheet of multiple choice questions and work on those!. Answers to warm-up (C C B D E) Homework Questions?. Computer Outputs. Finish Section 2.1. Density Curves. Always plot your data: dotplot , stemplot , histogram… Look for overall pattern (SOCS)

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Warm-Up

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  1. Warm-Up • Grab a sheet of multiple choice questions and work on those!

  2. Answers to warm-up (C C B D E)Homework Questions?

  3. Computer Outputs

  4. Finish Section 2.1

  5. Density Curves • Always plot your data: dotplot, stemplot, histogram… • Look for overall pattern (SOCS) • Calculate numerical summary to describe Add a step… • Sometimes the overall pattern is so regular we can describe it by a smooth curve. A Density Curve is a curve that: • Is always on or above the horizontal axis • Has an area of 1 underneath it

  6. Things to note… • The mean is the physical balance point of a density curve or a histogram • The median is where the areas on both sides of it are equal

  7. Don’t forget… • The mean and the median are equal for symmetric density curves!

  8. Start Section 2.2 Normal Curves!

  9. Normal Distributions = Normal Curves • Any particular Normal distribution is completely specified by two numbers: its mean () and standard deviation (). • We abbreviate the Normal distribution with mean and standard deviation as N()

  10. The 68-95-99.7 Rule

  11. Other images to explain the same thing…in case it helps!

  12. Example • A pair of running shoes lasts on average 450 miles, with a standard deviation of 50 miles. Use the 68-95-99.7 rule to find the probability that a new pair of running shoes will have the following lifespans. Between 400-500 miles More than 550 miles

  13. Warm-Up (09-26-13) On the driving range, Tiger Woods practices his golf swing with a particular club by hitting many, many golf balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 288 yards? What percent of Tiger’s drives travel between 296and 320yards?

  14. Example • The ACT and SAT are both Normally distributed with a mean of 18 and 1500 (respectively) and standard deviation of 6 and 300 (again respectively). Using this information find the following: • Percentage of scores that are above a 24 on the ACT. • Percentile for a 2100 on the SAT. • Percentage of ACT scores that are between 24 and 30. • Percentage of SAT scores that are between 900 and 1800.

  15. Example • A vegetable distributor knows that during the month of August, the weights of its tomatoes were normally distributed with a mean of 0.61 pound and a standard deviation of 0.15 pound. • What percent of the tomatoes weighed less than 0.76 pound? • In a shipment of 6000 tomatoes, how many tomatoes can be expected to weigh more than 0.31 pound? • In a shipment of 4500 tomatoes, how many tomatoes can be expected to weigh between 0.31 and 0.91 pound?

  16. How does this relate to z-scores? • If the distribution happens to be normal we can find the area under the curve and percentiles by using z-scores! • Standard Normal distribution – mean of 0 and standard deviation of 1.

  17. Table A in your book… • The table entry for each z-score is the area under the curve to the left of z. • If we wanted the area to the right, we would have to subtract from 1 or 100%

  18. Examples • Find the proportion of observations that are less than 0.81 • Find the proportion of observations that are greater than -1.78 • Find the proportion of observations that are less than 2.005 • Find the proportion of observations that are greater than 1.53 • Find the proportion of observations that are between -1.25 and 0.81

  19. Homework • Page 107: 19-38 (Density Curves) • Page 131: 41-54 (Normal Curves and z-scores)

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