A calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. find the probability of getting at least 70% of the questions correct?

The probability would be 0.000017.

70% of the 20 questions is 14 questions correct.  Using a binomial distribution for this, we have:

[tex]_{20}C_{14}(0.2)^{14}\times (1-0.2)^{20-14} \\ \\ \frac{20!}{14!6!}\times (0.2)^{14} \times (0.8)^6 \\ \\ \approx 0.000017 [/tex]