Answer to Question #308096 in Statistics and Probability for rutvik

Question

The proportion of eligible voters in the next corporation election (in tumkur) who will vote 

for the incumbent is assumed to be 55%. What is the probability that in a random sample of 

500 voters less than 49% say they will vote for the incumbent? Write your conclusion. 

Answer 1

we define the following

Assumptions/Conditions

Randomization: the 500 voters were chosen in a random sample

Independence: one person's vote does not affect another's

Sample Size: there are more than 5000 voters

Success/Failure:

np = (500)(0.55) > 10

nq = (500)(0.45) > 10

therefore we can use the normal model

mean = 0.55

standard deviation = ( (0.55*0.45)/500 )^1/2= 0.0222

N(0.55, 0.0222)

z = (0.49 - 0.55) / (0 .0222) = -2.703

according to the standard z-table, the probability that z<-2.703 is 0.0035 which equals (0.35%)

Hence we may conclude that there is a 0.35% probability that in a random sample of 

500 voters less than 49% say they will vote for the incumbent.