Mental health in schools. An NPR news article makes the following statement:6 “Up to one in five kids living in the U.S. shows signs or symptoms of a mental health disorder in a given year. So in a school classroom of 25 students, five of them may be struggling with the same issues many adults deal with: depression, anxiety, substance abuse.”Explain why the example cited can be described in the context of the binomial setting.The article cites three values (one in five, 25, five). What do they represent? Give both their mathematical symbol and their definition.Explain why the second sentence cited could be misinterpreted. Rewrite this sentence so that it is both mathematically correct and understandable for the general public.

Name: Mental health in schools. An NPR news article makes the following stat
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Mental health in schools. An NPR news article makes the following statement:6 “Up to one in five kids living in the U.S. shows signs or symptoms of a mental health disorder in a given year. So in a school classroom of 25 students, five of them may be

Introduction: The following are the general characteristics of a binomial distribution: Number of trials is fixed: The number of trials, say n, must be fixed. Trials are independent: The outcomes of the n trials are independent of each other. Trials may be classified as success and failure: Each of the n trials must result in either of two mutually exclusive, and exhaustive outcomes, which may be named as “success” and “failure”. Probability of success is constant: The probability of success, say p, remains constant from trial-to-trial; so does the probability of failure. The random variable X is usually defined as the number of successes in the n trials.1. Define X as the random variable representing the number of kids among a group of n = 25 kids, who show signs or symptoms of a mental health disorder. Now, verify the conditions as follows: Number of trials is fixed: The number of trials, that is, the number of students considered in the study is fixed at n = 25. Trials are independent: The mental health condition of one student in the classroom may be assumed to be independent of that of any other student, as they are not all members of the same family. Trials may be classified as success and failure: Since the researcher counts the number of students showing signs of mental health disorder, finding a student showing signs of mental health disorder may be considered to be a success, so that finding a student without signs of mental health disorder may be considered to be a failure. Probability of success is constant: It is known that one in five kids show signs of mental health disorder in the country. As a result, the probability of success, that is, the probability that a student shows signs of mental health disorder may be considered to be fixed at, say p = 1/5 = 0.20. Thus, the number of kids among a group of n = 25 kids, who show signs or symptoms of a mental health disorder may be considered to be a binomial distribution.2. The value “one in five” represents the fixed population proportion of kids living in the country who show signs of a mental health disorder. It is the probability of success in the binomial setup, given as p = 1/5. The value “25” represents the number of kids, that is, students considered for the study. It is the fixed number of trials in the binomial setup, given as n = 25. The value “5” represents the number of students expected to show signs of a mental health disorder among the 25 students considered in the study. In the binomial setup, for parameters n and p, the expected value of the random variable is, E (X) = np. Here, np = 25 ∙ (1/5) = 5.3. The second sentence is, “So in a school classroom of 25 students, five of them may be struggling with the same issues many adults deal with: depression, anxiety, substance abuse.” Statistically speaking, this sentence does not provide any wrong information, or misrepresentation of information; it is mentioned that five of them may be struggling with the issues. However, there is a strong possibility that the general public may fail to understand the importance of “may be” in this context, and understand it to mean that five students will be struggling with the issues. Instead of conveying the idea that 5 out of 25 students is expected to be observed with issues, one might misunderstand that 5 out of 25 students will surely be observed to have issues. In order to clear up unnecessary confusion, it can be rewritten, so that it is both mathematically correct and understandable for the general public, is, “So in a school classroom of 25 students, about five of them may be expected to be struggling with the same issues many adults deal with: depression, anxiety, substance abuse.”