Answer to Question #107607 in Statistics and Probability for Website is good

Question

A study reports that 5% of adults are afraid to be home alone at night. If 20 people are randomly selected, what is the probability at least 3 of them are afraid to be home alone at night ?
a) Is the situation Binomial or Hypergeometric ?
b) How do you know which one it is
c) Change the situation so that it could be calculated using other distribution ( for example , if it is binomial , change to hypergeometric )

Answer 1

a) This is Binomial

b) In the case of the binomial distribution, independence among trials is required.

On the other hand, the hypergeometric distribution does not require independence.

The Binomial situation sampled 20 people with the assumption that 5% are afraid to be home alone at night. 

c)Change

The Hypergeometric situation sampled 20 people from a total of 100 in which a random 5 are afraid to be home alone at night.