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Answer the following questions and show all work (including diagrams) to create a complete answer.

  1. Look at the following graphs and indicate whether they are binomial distributions, normal (standard) distributions, or exponential distributions. Explain how you know.
  2. Look at the following graphs and indicate whether they are binomial distributions, normal (standard) distributions, or exponential distributions. Explain how you know.
  3. It is determined that because of a particular genetic trend in a family, the probability of having a boy is 60%. Janet and David decide to have 4 children. What is the probability that they will have exactly 2 boys?
  4. For question 3, what is the probability that Janet and David will have at least 2 boys?
  5. For question 3, what is the probability that Janet and David will have at most 2 boys?
  6. The following data was collected on a recent 25-point math quiz. Does the data represent a normal distribution? Can you determine anything from the data? & 20 && 17 && 22 && 23 && 25\\& 14 && 15 && 14 && 17 && 9\\& 18 && 2 && 11 && 18 && 19\\& 14 && 21 && 19 && 20 && 18\\& 16 && 13 && 14 && 10 && 12
  7. A recent blockbuster movie was rated PG, with an additional violence warning. The manager of a movie theater did a survey of moviegoers to see what ages were attending the movie in an attempt to see if people were adhering to the warnings. Is his data normally distributed? Do moviegoers at the theater regularly adhere to warnings? & 17 && 9 && 20 && 27 && 16\\& 15 && 14 && 24 && 19 && 14\\& 19 && 7 && 21 && 18 && 12\\& 5 && 10 && 15 && 23 && 14\\& 17 && 13 && 13 && 12 && 14
  8. The heights of coniferous trees were measured in a local park in a regular inspection. Is the data normally distributed? Are there areas of the park that seem to be in danger? The measurements are all in feet. & 22.8 && 9.7 && 23.2 && 21.2 && 23.5\\& 18.2 && 7.0 && 8.8 && 25.7 && 19.4\\& 25.0 && 8.8 && 23.0 && 23.2 && 20.1\\& 23.1 && 18.5 && 21.7 && 21.7 && 9.1\\& 4.3 && 7.8 && 3.4 && 20.0 && 8.5
  9. Thomas is studying for his AP Biology final. In order to complete his course, he must do a self-directed project. He decides to swab a tabletop in the student lounge and test for bacteria growing on the surface. Every hour, he looks in his Petri dish and makes an estimate of the number of bacteria present. The following results were recorded.
Time (hr) Bacteria Count
0 1
1 6
2 40
3 215
4 1,300
5 7,800

Is this data representative of an exponential distribution? If so, find the equation. What is the count after 1 day?

  1. If you watch a grasshopper jump, you will notice the following trend:
Jump Number Distance (m)
1 4
2 2
3 1.1
4 0.51
5 0.25
6 0.13

Is this data representative of an exponential distribution? If so, find the equation. Why do you think the grasshopper's distance decreased with each jump?

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