# Quiz #10Name:I. The National institute of Mentai Health reports that there is a 30% chance of an aduit Americansuffering from a psychiatric disorder Three randomly selected adult Americans are examined for aPsychiatric disorders.aIf you let a success correspond to an aduit American having a psychiatric disorder, what is theSUCcess probability, p? (Note: The use if the word success in Bernaulli triais need nor reflect itsusually positive connotation.)PISuccess naving the psychiatric disorder)bConstruct a probability distribution table for three people examined using Binomial distribution.Let X be the number of adults who are suffering from the psychiatric disorder12TotalProbDetermine the mean and variance for the distribution.c)

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I missed my lecture today and i have no idea how to solve this problem.

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Step 1

Binomial distribution:

It is a discrete probability distribution that has exactly two outcomes for the experiment with probability of success, p and probability of failure, q. In binomial experiment, the probability of success over different trials remains constant. The probability distribution of binomial distribution is as follows:

Step 2

a) Success probability p:

It is given that 30% chance of an adult American suffering from a psychiatric disorder.

Here, n = 3.

The probability of success p corresponds to an adult American having a psychiatric disorder is obtained as p = 0.3, from the calculation given below.

Step 3

b) Probability distribution table for three people examined using Binomial distribution:

Here, x denotes the number of adults who are suffering from the psychiat...

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