Suppose that 53 of all registered voters prefer candidate Fe

Suppose that 53% of all registered voters prefer candidate Felicia Jones to candidate Janice Lomax for mayor of Port Charles.

a) In a random sample of 100 voters, what is the probability that the sample will indicate that Felicia Jones will win the election?

b) In a random sample of 100 voters, what is the probability that the sample will indicate that Felicia Jones will lose the election?

c) In a random sample of 100 voters, what is the probability that the sample will indicate a tie?

Solution

The above situation can be modelled by a Binomial distribution with n=100 and p= 0.53. Therefore, the probability distribution P(x) of the number x can be represented by

   P(X=x) =P(x) =n Cx p^x(1-p)^(n-x), x = 0,1,2,