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Variability in Probability

Variability in Probability. Thursday TWSSP. Agenda for Today. Chip Sampling Known Mixture Chip Sampling Unknown Mixture Cereal Boxes Wrap up Reflections Post Assessment GOALS Understand how to use variability to make predictions

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Variability in Probability

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  1. Variability in Probability Thursday TWSSP

  2. Agenda for Today • Chip Sampling Known Mixture • Chip Sampling Unknown Mixture • Cereal Boxes • Wrap up Reflections • Post Assessment • GOALS • Understand how to use variability to make predictions • Identify likely and unlikely results of experiments based on variability

  3. Chip Sampling • You will draw 30 samples of 10 chips, with replacement, from an opaque bag containing 70 blue chips and 30 orangechips. • What would you predict the results of those 30 samples would be? • Create a dot plot on chart paper showing your prediction.

  4. Chip Sampling • Gallery walk of dot plots • I notice, I wonder

  5. Chip Sampling • With your partner, take 30 samples of 10 chips, with replacement • Create a plot of your samples and post your plot below your prediction plot • I notice, I wonder • How did your expected range compare to your actual range?

  6. Chip Sampling • What is a likely range for the number of blue chips in a sample of 10? • How likely is it that no blues would occur in a sample? • How many samples do you think would need to be pulled to get at least one set of 10 with no blues in it?

  7. Real or Fake? • Mr. Pine’s class was doing the same project, and he stepped out of the classroom while they were running the simulation. When he came back, one group showed the graph below. Do you think it represents real data, or did they make it up?

  8. Chip Sampling • At your table, you have a collection of a large number of chips (significantly more than 100) in two colors. • Devise a sampling plan to determine the proportion of each color chip in the mix. Please do not exceed a sample size of 20 chips. • Carry out your plan

  9. Chip Sampling • Based on the results of your sample, what do you believe the proportion of chips of each color to be? • Be prepared to share and defend your sampling plan, and justify your decision about the mixture. • What mixture proportions would be surprising to you? What would not?

  10. Cereal Boxes • A cereal brand is giving away 6 different toys, with one toy in each box of cereal. The company says the different toys are evenly distributed over the cereal boxes. • How many boxes do you think you would have to buy in order to get all 6 toys? • Devise a simulation to test this.

  11. Cereal Boxes • Carry out your simulation and come to a conclusion about the number of cereal boxes you would need to buy. • Prepare a graphical display to report your results and prepare to defend your conclusion.

  12. Cereal Boxes • Ms. Kim suspects that one of her two classes made up data on the cereal boxes activity. Which of the two below do you think is more likely to have been made up?

  13. Exit Ticket (sort of…) • Suppose there is a mixture of 60% blue and 40% yellow chips. What would be a likely range for the number of blues drawn in 30 samples of 10 chips? How many draws do you think it would take to get no blues? • Suppose you have 5 different kinds of cereal and each morning you choose one type at random for breakfast. How many days do you think it would take until you have had each kind at least once for breakfast?

  14. Wrap Up • I notice, I wonder about variability • Why do you think it is important to understand variability? • How, if at all, has your thinking about variability changed this week? • What do you still want to know about variability? • What do you still want to know about probability and statistics? • What implications might some of what you learned this week have for your own teaching?

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