question:the claimed germination rate of seeds in a packet is 90%. a gardener suspects the real rate is not as high as it is claimed so he carries out a trial. he selects 120 seeds and 97 germinate. test to see if his suspicions are well founded by using a confidence interval for the population portion at the 5% significance level.

so what i would of thought the right answer would be is saying the population portion=97/120 and then using the formula margin of error formula 1/√120 la . +/- this to the population portion but apparently this is wrong. apparently you have to use the formula √[(p(1-p))/n] i have no idea where this formula comes from and why you have to use it. I was only thought about the 1/√n formula so 1 what is this formula? 2 why do you use it here? and 3 how can I tell which formula to use ?

thanks