A candidate for governor has his campaign sample 100 voters

A candidate for governor has his campaign sample 100 voters to gauge his support. Assuming he has 52% support in the voting population, what is the probability that in his sample of 100, 48% or less will say they support him? (Hint: Use the normal approximation to the binomial for the sampling distribution.)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < = 48) = Using Excel Formula = ROUND(BINOMDIST(48,100,0.52,TRUE),4)
= 0.24167