Question

a psychologist found a study which claiming that 32% of patients who visit a psychologist have symptoms of anxiety. this psychologist had 37 patients visit. let x = the number of patients that had symptoms of anxiety. (a) the random variable is which of the following? the number of patients without symptoms of anxiety the number of patients who visited the psychologist the number of patients who had symptoms of anxiety the number of psychologists (b) how many total patients did the psychologist have visit? (c) determine whether the following statement is true or false. this scenario is an example of a binomial probability distribution. true false

Explanation:

(a)

Step1: Understand random variable definition

A random variable is a variable whose value is determined by the outcome of a random event. Here, \(x\) is defined as the number of patients that had symptoms of anxiety.

Step2: Analyze each option

• "the number of patients without symptoms of anxiety": Not what \(x\) is defined as.
• "the number of patients who visited the psychologist": Given as 37, not a random variable here (already fixed number).
• "the number of patients who had symptoms of anxiety": Matches the definition of \(x\).
• "the number of psychologists": Only 1 psychologist mentioned.

(b)

Step1: Extract information from text

The text states "This psychologist had 37 patients visit".

(c)

Step1: Check binomial distribution criteria

Binomial distribution has: fixed number of trials (\(n = 37\) patients - fixed), two possible outcomes (has anxiety symptoms or not), independent trials (assuming patient visits are independent), and constant probability (\(p=0.32\) - given).

Answer:

(a) the number of patients who had symptoms of anxiety
(b) 37
(c) True