The census bureau reports that 29% of California residents were born outside of the US. Suppose that you choose four Californians independent of each other.

Question

Let F= the number of foreign-born people in a randomly-selected group of four. 

a)Find P(f=1)

b)Find P(f>or =1)

c)find and interpret the expected value of F.

d)find and interpret the standard deviation of F

Answer 1

This is a binomial setting therefore you can find c) and d) very easily

 

np  = 4(.29) = 1.16    Expected Value        On average we would find 1.16 foreign-born people from a group of 4 people if we keep picking groups of 4 over and over again

 

sqrt(np(1-p)) = sqrt(.8236) = .9075241044   Standard Deviation (the typical distance a value of  f differs from 1.16

 

 

a) There is 4 ways to pick 1 out of 4 so we have    4(.29)(.71)^3 = .41517676 = 41.517676%

 

b) Easier to do P(F = 0) and subtract from 100%

 

There is only 1 way to get 0 so we have     1(.29)^0(.71)^4  =.25411681   Now subtract from 1   74.588319%