The track coach at a high school needs a student whose reaction time is less than 0.4 seconds to help out at track meets. All the twelfth graders in the school measured their reaction times. Your teacher will give you a bag of papers that list their results.

1. Work with your partner to select a random sample of 20 reaction times, and record them in the table.
2. What proportion of your sample is less than 0.4 seconds?
3. Estimate the proportion of all twelfth graders at this school who have a reaction time of less than 0.4 seconds. Explain your reasoning.
4. There are 120 twelfth graders at this school. Estimate how many of them have a reaction time of less than 0.4 seconds.

5. Suppose another group in your class comes up with a different estimate than yours for the previous question.

   1. What is another estimate that would be reasonable?

   2. What is an estimate you would consider unreasonable?

Here are the results of a survey of 20 people who read The Adventures of Super Sam regarding what special ability they think the new hero should have.

• fly
• freeze
• freeze
• fly
• fly
• freeze
• fly
• strength
• freeze
• fly
• freeze
• freeze
• fly
• invisibility
• freeze
• fly
• freeze
• fly
• strength
• freeze

1. What proportion of this sample wants the new hero to have the ability to fly?
2. If there are 2,024 dedicated readers of The Adventures of Super Sam, estimate the number of readers who want the new hero to fly.

3. Two other comic books did a similar survey of their readers.

   • In a survey of people who read Beyond Human, 42 out of 60 people want a new hero to be able to fly.
   • In a survey of people who read Mysterious Planets, 14 out of 40 people want a new hero to be able to fly.

   Do you think the proportion of all readers who want a new hero that can fly are nearly the same for the three different comic books? Explain your reasoning.

4. If you were in charge of these three comics, would you give the ability to fly to any of the new heroes? Explain your reasoning using the proportions you calculated.

The authors of The Adventures of Super Sam chose 50 different random samples of readers. Each sample is of size 20. They look at the sample proportions who prefer the new hero to fly.

<p>A dot plot for “sample proportions for The Adventures of Super Sam” with the numbers 0 point 1 through 0 point 55, in increments of zero point zero 5, indicated. The data are as follows: 0 point 1, 3 dots. 0 point 1 5, 3 dots. 0 point 2, 11 dots. 0 point 2 5, 10 dots. 0 point 3, 8 dots. 0 point 3 5, 7 dots. 0 point 4, 4 dots. 0 point 4 5, 2 dots. 0 point 5, 1 dot. 0 point 5 5, 1 dot.</p>  

1. What is a good estimate of the proportion of all readers who want the new hero to be able to fly?
2. Are most of the sample proportions within 0.1 of your estimate for the population proportion?

3. If the authors of The Adventures of Super Sam give the new hero the ability to fly, will that please most of the readers? Explain your reasoning.

4. The authors of the other comic book series created similar dot plots.

   

   <p>A dot plot for “sample proportions for Beyond Human” with the numbers 0 point 6 through 0 point 8 5, in increments of zero point zero 5, indicated. The data are as follows: 0 point 6 3, 1 dot. 0 point 6 5, 2 dots. 0 point 6 7, 3 dots. 0 point 6 9, 4 dots. 0 point 7, 5 dots. 0 point 7 2, 6 dots. 0 point 7 4, 6 dots. 0 point 7 5, 5 dots. 0 point 7 7, 7 dots. 0 point 7 8, 6 dots. 0 point 8, 3 dots 0 point 8 2, 1 dot. 0 point 8 4, 1 dot.</p>  

     

   

   <p>A dot plot for “sample proportions for Mysterious Planets” with the numbers 0 point 3 through 0 point 7, in increments of 0 point 5, indicated. The data are as follows: 0 point 3 3, 1 dot. 0 point 3 5, 2 dots. 0 point 3 8, 5 dots. 0 point 4, 2 dots. 0 point 4 3, 6 dots. 0 point 4 5, 4 dots. 0 point 4 8, 7 dots. 0 point 5, 3 dots. 0 point 5 3, 6 dots. 0 point 5 5, 5 dots. 0 point 6, 3 dots. 0 point 6 3, 2 dots. 0 point 6 5, 2 dots. 0 point 6 7, 2 dots.</p>  

   For each of these series, estimate the proportion of all readers who want the new hero to fly.

   • Beyond Human:
   • Mysterious Planets:
5. Should the authors of either of these series give their new hero the ability to fly?
6. Why might it be more difficult for the authors of Mysterious Planets to make the decision than the authors of the other series?