Part 1: what are the conditions for using the standard deviation formula when conducting a significance test? be specific about p versus p-hat. part 2: what are the conditions for approximating with a normal distribution? '

The conditions that must be met when using the standard deviation formula when conducting a significance test are that the samples should be independent of each other and the variance is known and not infinite.
The difference between p and p-hat is that p represents that true standard deviation of the population while p-hat is only an approximation using a sample of the population. 
The conditions that must be met when approximating a normal distribution are that the samples must be independent of each other and that number of samples must be at least 30.

Im not that good with division but i think 5 is -6but dont quote me on thatim not the best in division but thats my answer