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Applet Exercises

Applet Exercises

To do these exercises, go to www.macmillanhighered.com/fapp10e.

Question 5.104

1. The Mean and Median applet allows you to place observations on a line and see their mean and median visually.

  1. Place two observations on the line by clicking below it. Why does only one arrow appear?
  2. Now move the rightmost point close to the other point. (Place the cursor on the point, hold down the mouse button, and drag the point.) Add a third point that is somewhat to the right of the other two. Pull the single rightmost observation out to the right. How does the mean behave? How does the median behave? Explain briefly why each measure acts as it does.

Question 5.105

2. In Example 19 (page 217), we used the fact that SAT section scores are close to normal and are adjusted so that the mean is close to 500 and the standard deviation is close to 100. (Actual scores in a particular year have a slightly different mean and standard deviation.) Use the Normal Density Curve applet with mean μ=500 and standard deviation σ=100 to answer these questions:

  1. What proportion of SAT scores is above 640? (You may want to uncheck the 2-Tail box.)
  2. What proportion of SAT scores is between 420 and 640? (If you drag one flag across the other, the applet shows the area between the flags.)

Question 5.106

3. Because Internet browsers have limited resolution, the Normal Density Curve applet can’t always get exactly the values you want. Use the applet as set in the previous exercise to come close to exact answers to these questions.

  1. How high must an SAT score be to fall in the top 10% of all scores?
  2. How high must an SAT score be to fall in the top 1% of all scores?

Question 5.107

4. The 68-95-99.7 rule for normal distributions is a useful approximation. You can use the Normal Density Curve applet to see how accurate the rule is. Drag one flag across the other so that the applet shows the area under the curve between the two flags.

  1. Place the flags 1 standard deviation on either side of the mean. What is the area between these two values? What does the 68-95-99.7 rule say this area is?
  2. Repeat for locations 2 and 3 standard deviations on either side of the mean. Again, compare the 68-95-99.7 rule with the area given by the applet.
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