Question

Suppose just two-thirds of all voters support a certain proposition. 800 voters are chosen at random. Find the probability that a majority of these 800 oppose the proposition.

Answer in back of book: 7.6x10^-24

Explanations and work please

Answer 1

Proportion that oppose the proposition = 1 - 2/3 = 1/3

n=800

Std error , SE = √( p(1-p)/n ) =    0.0167      
          
sample proportion , p̂ > 0.50   
Z=( p̂ - p )/SE=    (0.5-0.3333)/0.0167)=       10.00
P ( p̂ >    0.5   ) =P(Z > ( p̂ - p )/SE) =P(Z >   10.000   ) = P(Z<-10) =  7.6E-24 or 7.6*10^-24

excel formula: "=normsdist(-10.00)"