Question 5.103

73. If you ask a computer (or your graphing calculator) to generate "random numbers" between 0 and 1, you will get data from a uniform distribution. Figure 5.37 shows a graph of the density curve for this distribution.

  1. Check that the area under the uniform density curve is 1.
  2. What is the mean of this distribution?
  3. What proportion of outcomes from this distribution lie between 0.2 and 0.8?
  4. What percentage of random numbers between 0 and 1 would you expect to lie between 0 and 0.5?
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Figure 5.39: Figure 5.37 For Exercise 73, density curve for the uniform distribution.

73.

(a) Since the uniform density curve forms a rectangle, the area is found by multiplying the length of the rectangle by its height: .

(b) —that's the balance point for the region under the density function.

(c) Area under the density curve over this interval is . (Since it is rectangular in shape, just multiply width times height.)

(d) 50%