Mental health in America. In the Mental Health Surveillance Study, clinicians interviewed a very large random sample of American adults so as to diagnose the presence of mental disorders in the prior 12 months. There are many types of mental disorders, and a person can suffer from more than one. Let X represent the number of mental disorders a person has experienced in the past year. Based on this study, we can assign the following probability distribution to X in the American adult population: X 0 1 2 3 4 or more
P(X) 0.775 0.149 0.041 0.022 0.013
(a) Explain why this is a valid probability distribution. Is the sample space discrete orcontinuous?
(b) Find P(X <2) and P(1≤X≤3).
(c) Obtain the probability that a randomly selected American adult suffers from
(i) at least one mental disorder
(ii) either one or two mental disorders

a) It is a valid distribution because the sum of all possible probabilities is 1. The sample space is discrete, because the number of diseases is a countable number.

b) P(X <2) = 0.924, P(1≤X≤3) = 0.212

c - i) 0.225

c - ii) 0.19

Step-by-step explanation:

(a) Explain why this is a valid probability distribution. Is the sample space discrete or continuous?

0.775 + 0.149 + 0.041 + 0.022 + 0.013 = 1

Since the sum of all possible probabilities is 1, this is a valid probability distribution.

Since the possible outcomes are 0, 1, 2, 3 or 4 diseases, that is, countable numbers, the sample space is discrete.

(b) Find P(X <2) and P(1≤X≤3).

(c) Obtain the probability that a randomly selected American adult suffers from

(i) at least one mental disorder

(ii) either one or two mental disorders

15 units use socratic

step-by-step explanation: 15 units

i believe the answer is letter c) 8

step-by-step explanation: