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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Asked Sep 28, 2019
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I missed my lecture today and i have no idea how to solve this problem.

Quiz #10
Name:
I. The National institute of Mentai Health reports that there is a 30% chance of an aduit American
suffering from a psychiatric disorder Three randomly selected adult Americans are examined for a
Psychiatric disorders.
a
If you let a success correspond to an aduit American having a psychiatric disorder, what is the
SUCcess probability, p? (Note: The use if the word success in Bernaulli triais need nor reflect its
usually 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 disorder
1
2
Total
Prob
Determine the mean and variance for the distribution.
c)
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Quiz #10 Name: I. The National institute of Mentai Health reports that there is a 30% chance of an aduit American suffering from a psychiatric disorder Three randomly selected adult Americans are examined for a Psychiatric disorders. a If you let a success correspond to an aduit American having a psychiatric disorder, what is the SUCcess probability, p? (Note: The use if the word success in Bernaulli triais need nor reflect its usually 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 disorder 1 2 Total Prob Determine the mean and variance for the distribution. c)

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Expert Answer

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:

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(n-x) "C,p (1-p)-) where, n is the number of trials, x is the possible random variable, and p is the probability of success

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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.

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30 р3 100 =0.3

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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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P(x0)=C,(0.3)'(1-0.3)-) 0.343 P(x-1) C(0.3)(1-0.3)-) 0.3)3-1) =0.441 (3-2) P(x-2)C,(0.3) (1-0.3)6-2) = 0.189 (3-3) P(x3)C(0.3) (1-0.3)6-) = =0.027 Probability distribution table: Total 0 1 2 3 x Prob.0.343 | 0.441 | 0.189 0.027 1

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