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Identifying a Probability Distribution

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Learning is a lifetime activity. For some, it means learning from everyday experiences; for others, it means taking classes in a more traditional atmosphere. The percentage of people participating in organized learning situations during 2002 for each age group is reported here by NIACE.
Is this a probability distribution? Explain why or why not.

Age group: 17-19 20-24 25-35 35-44 45-54 55-64 65-74 75+ All
Percentage: 78 72 51 49 44 30 20 10 42
Source: NIACE Adult Participation in Learning Surveys

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A probability distribution gives the probability for each value of the random variable. It can be displayed in the form of a ...

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This solution shows you how to decide if a given data is a probability distribution or not.`

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5. To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.

A. List the experimental outcomes associated with performing the blood analysis.

B. If the random variable of interest is the total number of steps required to do the complete analysis (both procedures), show what value the random variable will assume for each of the experimental outcomes?

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 educational programs until they fall behind by approximately two years' worth of learning, and that typically means third grade or later (usa today sept. 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)

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