For Exercise 1.70, see page 40; for 1.71 to 1.73, see pages 41-42; for 1.74 to 1.77, see pages 44-45; for 1.78, see page 46; for 1.79 and 1.80, see page 49; for 1.81 and 1.82, see page 50; and for 1.83 and 1.84, see page 53.

Question 1.72

1.72 A uniform distribution.

Figure 1.20 displays the density curve of a uniform distribution. The curve takes the constant value 1 over the interval from 0 to 1 and is 0 outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1. Use areas under this density curve to answer the following questions.

uniform distribution

  1. What percent of the observations lie above 0.7?
  2. What percent of the observations lie below 0.4?
  3. What percent of the observations lie between 0.45 and 0.70?
  4. Why is the total area under this curve equal to 1?
  5. What is the mean of this distribution?