Researchers are concerned about the rise in gun violence in their community amon

Question

Researchers are concerned about the rise in gun violence in their community among the adolescent population. Suppose the researchers believe that this rise in violence is due to an increase in depressive symptoms among the demographic aged 11-17. Suppose the researchers estimate that only 11% of this population suffers from depressive-like symptoms.

a) What is the probability of finding no one with depressive-like symptoms in a sample of 8?

b) What is the probability that at least 3 respondents of a sample of 8 report these symptoms?

What is the expected number of adolescents in the sample to report the symptoms?

Explanation / Answer

Ans:

Binomial distribution with n=8,p=0.11

a)P(x=0)=8C0*0.110*(1-0.11)8

=0.898

=0.3937

b)P(x>=3)=1-P(x<=2)=1-0.898-8C1*0.111*0.897-8C2*0.112*0.896

=1-0.3937-0.3892-0.1684

=0.0487

Expected number of adolescents=np=8*0.11=0.88

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