Probability + normal distribution

so my take-home quiz consists of a problem that i haven't been able to figure out, and i met similar frustration from my classmates as well.

we are studying normal distribution as of now, and what seems a binomial problem this is a hard nut to crack:

" a multiple choice test consists of 60 questions. each question has 4 possible answers of which one is correct. if all answers are random guesses, estimate the probability of getting at least 20% correct. "

also, the instructions indicate to find the probability using the normal distribution as an approximation to the binomial distribution.

my guesses are as follows:

1. find z-score and use table, but i think it's out of the question to calculate standard deviation in this case

2. use normalpdf or binomial pdf using TI-83 (n=60, p=.25) but really, have no idea where to go from there

3. make a chart of x and P(x), or all outcomes on my TI-83 with binomial values and calculate standard deviation.

please lead me in the right direction. i don't really need the answer, i just need to figure out how to get it!

thank you in advance