Question

If I take binomial distribution, like P % a population are graduates.

Given a sample of Size n, i get p% of as graduates .

Can we have a special case equations to find,

for give n, probability of P-p < Threshold ?
Lets Say n=600 , and P-p <= 1 % ie 6 .

Answer 1

The Population proportion = P% = P/100

The sampling distribution of a sample will follow a normal distribution irrespect to whatever the population distribution is. This is called normal approximation to binomal.

The sample follows a normal distribution with,

where n is the sample size and p is sample proportion of graduate student.

Now the probability,

The threshold value of P-p is 6.

To calculate the probabilty first convert the normal distribution to standard normal as,