Question 880572
This is a sampling distribution of proportion, we know
sample size is 100 and P(probability of taking vaccination) = .25 and Q(probability of not taking vaccination) = .75
mean of p is .25 and standard deviation of p is square root (PQ/ n) where n is the sample size, therefore
standard deviation of p is square root ((.25 * .75)/ 100) = 0.04330127
now 20/100 = .20
calculate the z value = (.20 - .25) / 0.04330127 = −1.154700543
consult table of z values for probability associated with the z value
therefore P(X<20) is 0.1251