Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of these children have reading problems that should be identified and corrected before third grade. Current federal law prohibits most children from receiving extra help from special education programs until they fall behind by approximately two years' worth of learning, and that typically means third grade or later (USA Today,
September 6, 2001).
Age Number of Children
6 ............ 37,369
7 ............ 87,436
8 ............160,840
9 ............239,719
10 .............286,719
11 .............306,533
12 .............310,787
13 .............302,604
14 .............289,168
Suppose that we want to select a sample of children identified as learning disabled under special education for a program designed to improve reading ability. Let x be a random variable indicating the age of one randomly selected child.
a. Use the data to develop a probability distribution for x. Specify the values for the random variable and the corresponding values for the probability function f (x).
b. Draw a graph of the probability distribution.
c. Show that the probability distribution satisfies equations (5.1) and (5.2).