Final answer:
The random variable X is the number of adult Americans who believe crime is the main problem, while P' is the sample proportion estimate of this belief.
Step-by-step explanation:
In the context provided by a national magazine reporting on a telephone poll of 1,000 adult Americans, the random variable X represents the number of adult Americans who believe that crime is the main problem facing the country. The random variable P' (pronounced P-prime) refers to the proportion of the sample that believes crime is the main problem facing the country, which is an estimate of the true population proportion.
In this telephone poll, if 20% of the respondents, or 200 out of 1,000, indicated that crime is the main problem, then X would be 200. The sample proportion P' could be calculated by dividing X by the total number of respondents (n), giving us P' = X/n = 200/1000 = 0.20 or 20%.