# Probability and Expected Value of Literacy

9.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.

19. The National Basketball Association (NBA) records a variety of statistics for each team. Two of these statistics are the percentage of field goals made by the team and the percentage of three-point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in the NBA showed the probability of scoring three points by making a field goal was .44, and the probability of scoring two points whot was .34(http://www.nba.com,January 3,2004).

a. What is the expected value of a two-point shot for these teams?

b. What is the expected value of a three-point shot for these teams?

c. If the probability of making a two-point shot is greater than the probability of making a three-point shot, why do coaches allow some players to shoot the three-point shot if they have the oppoturnity? Use expected value to explain your answer.

31. Nine percent of undergraduate students carry credit card balances greater than $7000(Reader's Digest,July 2002). Suppose 10 undergraduate students are selected randomly to be interviewed about credit card usage.

a. Is the selection of 10 students a binominal experiment? Explain.

b. What is the probability that two of students will have a credit card balance greater than $7000.

c. What is the probability that none will have a credit card balance greater than $7000

d. What is the probability that at least three will have a credit card balance greater than $7000.

#### Solution Summary

All the three questions in the file solved systematically showing all steps.